:: VECTSP_8 semantic presentation

begin

definition
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let VS be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
func lattice VS -> ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) equals :: VECTSP_8:def 1
 LattStr(# (Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(SubJoin VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( Function-like V21([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) , Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) : ( ( ) ( ) set ) ) ) ( non empty V7() V10([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) ) V11( Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) : ( ( ) ( ) set ) ) Function-like V17([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) ) V21([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) , Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) : ( ( ) ( ) set ) ) ) Element of bool [:[:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) ,(SubMeet VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( Function-like V21([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) , Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) : ( ( ) ( ) set ) ) ) ( non empty V7() V10([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) ) V11( Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) : ( ( ) ( ) set ) ) Function-like V17([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) ) V21([:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) , Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) : ( ( ) ( ) set ) ) ) Element of bool [:[:(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) ,(Subspaces VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) : ( ( ) ( ) set ) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) #) : ( ( strict ) ( strict ) LattStr ) ;
end;

definition
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let VS be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
mode SubVS-Family of VS -> ( ( ) ( ) set ) means :: VECTSP_8:def 2
 for x being ( ( ) ( ) set ) st x : ( ( ) ( ) set ) in it : ( ( Function-like V21([:F : ( ( ) ( ) LattStr ) ,F : ( ( ) ( ) LattStr ) :] : ( ( ) ( V7() ) set ) ,F : ( ( ) ( ) LattStr ) ) ) ( V7() V10([:F : ( ( ) ( ) LattStr ) ,F : ( ( ) ( ) LattStr ) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( ) ( ) LattStr ) ) Function-like V21([:F : ( ( ) ( ) LattStr ) ,F : ( ( ) ( ) LattStr ) :] : ( ( ) ( V7() ) set ) ,F : ( ( ) ( ) LattStr ) ) ) Element of bool [:[:F : ( ( ) ( ) LattStr ) ,F : ( ( ) ( ) LattStr ) :] : ( ( ) ( V7() ) set ) ,F : ( ( ) ( ) LattStr ) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) holds
x : ( ( ) ( ) set ) is ( ( ) ( non empty V71() V108(F : ( ( ) ( ) LattStr ) ) V109(F : ( ( ) ( ) LattStr ) ) V110(F : ( ( ) ( ) LattStr ) ) V111(F : ( ( ) ( ) LattStr ) ) V118() V119() V120() ) Subspace of VS : ( ( ) ( ) VectSpStr over F : ( ( ) ( ) LattStr ) ) ) ;
end;

registration
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let VS be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
cluster non empty for ( ( ) ( ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ;
end;

definition
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let VS be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
:: original: Subspaces
redefine func Subspaces VS -> ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ;
let X be ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ;
:: original: Element
redefine mode Element of X -> ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ;
end;

definition
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let VS be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
let x be ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Element of Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) ;
func carr x -> ( ( ) ( ) Subset of ) means :: VECTSP_8:def 3
 ex X being ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) st
( x : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) = X : ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) & it : ( ( ) ( ) Element of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) = the carrier of X : ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) );
end;

definition
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let VS be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
func carr VS -> ( ( Function-like V21( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) , bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty V7() V10( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ) V11( bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) Function-like V17( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ) V21( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) , bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) Function of Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) , bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) means :: VECTSP_8:def 4
 for h being ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) Element of Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) )
for H being ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) st h : ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Element of Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) = H : ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) holds
it : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . h : ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Element of Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) : ( ( ) ( ) Element of bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) = the carrier of H : ( ( ) ( non empty V71() V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ;
end;

theorem :: VECTSP_8:1
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for H being ( ( non empty ) ( non empty ) Subset of ( ( ) ( non empty ) set ) ) holds not (carr VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( Function-like V21( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) , bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty V7() V10( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) V11( bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) Function-like V17( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) V21( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) , bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) Function of Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) , bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) .: H : ( ( non empty ) ( non empty ) Subset of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) is empty ;

theorem :: VECTSP_8:2
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for H being ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) holds 0. VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( V50(b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) Element of the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) in (carr VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( Function-like V21( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) , bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty V7() V10( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) V11( bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) Function-like V17( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ) V21( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) , bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) Function of Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) , bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . H : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( ) set ) ;

definition
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let VS be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
let G be ( ( non empty ) ( non empty ) Subset of ( ( ) ( non empty ) set ) ) ;
func meet G -> ( ( strict ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) means :: VECTSP_8:def 5
 the carrier of it : ( ( ) ( ) Element of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) : ( ( ) ( ) set ) = meet ((carr VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) : ( ( Function-like V21( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) , bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty V7() V10( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ) V11( bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) Function-like V17( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ) V21( Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) , bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) Function of Subspaces VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( non empty ) ( non empty ) SubVS-Family of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) , bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) .: G : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) Element of bool (bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of bool the carrier of VS : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ;
end;

theorem :: VECTSP_8:3
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) holds Subspaces VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty ) ( non empty ) SubVS-Family of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) = the carrier of (lattice VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ;

theorem :: VECTSP_8:4
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) holds the L_meet of (lattice VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( Function-like V21([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V11( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V21([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Element of bool [:[: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) : ( ( ) ( non empty ) set ) ) = SubMeet VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( Function-like V21([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V11( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V21([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [:[:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) : ( ( ) ( non empty ) set ) ) ;

theorem :: VECTSP_8:5
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) holds the L_join of (lattice VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( Function-like V21([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V11( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V21([: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Element of bool [:[: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) : ( ( ) ( non empty ) set ) ) = SubJoin VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( Function-like V21([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V11( Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ) V21([:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) , Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [:[:(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) ,(Subspaces b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) : ( ( ) ( non empty ) set ) ) ;

theorem :: VECTSP_8:6
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for p, q being ( ( ) ( ) Element of ( ( ) ( non empty ) set ) )
for H1, H2 being ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) st p : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) = H1 : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) & q : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) = H2 : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) holds
( p : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) [= q : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) iff the carrier of H1 : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) c= the carrier of H2 : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) ) ;

theorem :: VECTSP_8:7
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for p, q being ( ( ) ( ) Element of ( ( ) ( non empty ) set ) )
for H1, H2 being ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) st p : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) = H1 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) & q : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) = H2 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) holds
p : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) "\/" q : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) = H1 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) + H2 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ;

theorem :: VECTSP_8:8
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for p, q being ( ( ) ( ) Element of ( ( ) ( non empty ) set ) )
for H1, H2 being ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) st p : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) = H1 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) & q : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) = H2 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) holds
p : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) "/\" q : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) = H1 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) /\ H2 : ( ( ) ( non empty V71() V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) ;

definition
let L be ( ( non empty ) ( non empty ) LattStr ) ;
redefine attr L is complete means :: VECTSP_8:def 6
 for X being ( ( ) ( ) Subset of ) ex a being ( ( ) ( ) Element of ( ( ) ( non empty non trivial ) set ) ) st
( a : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) is_less_than X : ( ( ) ( ) Subset of ) & ( for b being ( ( ) ( ) Element of ( ( ) ( non empty non trivial ) set ) ) st b : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) is_less_than X : ( ( ) ( ) Subset of ) holds
b : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) [= a : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) ) );
end;

theorem :: VECTSP_8:9
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) holds lattice VS : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) is complete ;

theorem :: VECTSP_8:10
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for x being ( ( ) ( ) set )
for VS being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for S being ( ( ) ( ) Subset of ) st not S : ( ( ) ( ) Subset of ) is empty & S : ( ( ) ( ) Subset of ) is linearly-closed & x : ( ( ) ( ) set ) in Lin S : ( ( ) ( ) Subset of ) : ( ( strict ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) holds
x : ( ( ) ( ) set ) in S : ( ( ) ( ) Subset of ) ;

definition
let F be ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ;
let A, B be ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ;
let f be ( ( Function-like V21( the carrier of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of B : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of B : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ;
func FuncLatt f -> ( ( Function-like V21( the carrier of (lattice A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice B : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of (lattice A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice B : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of (lattice A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice B : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of (lattice A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice B : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) means :: VECTSP_8:def 7
 for S being ( ( strict ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) Subspace of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) )
for B0 being ( ( ) ( ) Subset of ) st B0 : ( ( ) ( ) Subset of ) = f : ( ( ) ( ) Element of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) .: the carrier of S : ( ( strict ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) Element of bool the carrier of B : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) holds
it : ( ( Function-like V21([: the carrier of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ,A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) :] : ( ( ) ( V7() ) set ) ,A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ) ( V7() V10([: the carrier of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ,A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) :] : ( ( ) ( V7() ) set ) ) V11(A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Function-like V21([: the carrier of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ,A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) :] : ( ( ) ( V7() ) set ) ,A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ) Element of bool [:[: the carrier of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ,A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) :] : ( ( ) ( V7() ) set ) ,A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . S : ( ( strict ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) Subspace of A : ( ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( ) ( ) set ) = Lin B0 : ( ( ) ( ) Subset of ) : ( ( strict ) ( non empty V71() strict V108(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) Subspace of B : ( ( Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) ) ;
end;

definition
let L1, L2 be ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ;
mode Semilattice-Homomorphism of L1,L2 -> ( ( Function-like V21( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) , the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ) V11( the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ) V21( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) , the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) , the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) means :: VECTSP_8:def 8
 for a, b being ( ( ) ( ) Element of ( ( ) ( non empty non trivial ) set ) ) holds it : ( ( Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . (a : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) "/\" b : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) = (it : ( ( Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . a : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) "/\" (it : ( ( Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . b : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) ;
end;

definition
let L1, L2 be ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ;
mode sup-Semilattice-Homomorphism of L1,L2 -> ( ( Function-like V21( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) , the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ) V11( the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ) V21( the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) , the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) , the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) means :: VECTSP_8:def 9
 for a, b being ( ( ) ( ) Element of ( ( ) ( non empty non trivial ) set ) ) holds it : ( ( Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . (a : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) "\/" b : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) : ( ( ) ( non empty non trivial ) set ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) = (it : ( ( Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . a : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) "\/" (it : ( ( Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) ( V7() V10([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ) V11(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) Function-like V21([:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) ) Element of bool [:[:L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) ,L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) :] : ( ( ) ( V7() ) set ) : ( ( ) ( non empty ) set ) ) . b : ( ( ) ( ) Element of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of the carrier of L2 : ( ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) ( non empty V71() strict V108(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V109(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V110(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V111(L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) V118() V119() V120() ) VectSpStr over L1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) L11()) ) : ( ( ) ( non empty ) set ) ) ;
end;

theorem :: VECTSP_8:11
for L1, L2 being ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice)
for f being ( ( Function-like V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of L1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of L2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) holds
( f : ( ( Function-like V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) is ( ( ) ( non empty V7() V10( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) Homomorphism of L1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ,L2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ) iff ( f : ( ( Function-like V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) is ( ( ) ( non empty V7() V10( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) sup-Semilattice-Homomorphism of L1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ,L2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ) & f : ( ( Function-like V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) is ( ( ) ( non empty V7() V10( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of b1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) : ( ( ) ( non empty ) set ) ) ) Semilattice-Homomorphism of L1 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ,L2 : ( ( non empty Lattice-like ) ( non empty join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like ) Lattice) ) ) ) ;

theorem :: VECTSP_8:12
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for A, B being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for f being ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) st f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is additive & f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is homogeneous holds
FuncLatt f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) : ( ( Function-like V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) is ( ( ) ( non empty V7() V10( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) sup-Semilattice-Homomorphism of lattice A : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) , lattice B : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) ) ;

theorem :: VECTSP_8:13
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for A, B being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for f being ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) st f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is one-to-one & f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is additive & f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is homogeneous holds
FuncLatt f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) : ( ( Function-like V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) is ( ( ) ( non empty V7() V10( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Homomorphism of lattice A : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) , lattice B : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) ) ;

theorem :: VECTSP_8:14
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for A, B being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) )
for f being ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) st f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is additive & f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is homogeneous & f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) is one-to-one holds
FuncLatt f : ( ( Function-like V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Function of ( ( ) ( non empty ) set ) , ( ( ) ( non empty ) set ) ) : ( ( Function-like V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b3 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) is one-to-one ;

theorem :: VECTSP_8:15
for F being ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field)
for A being ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of F : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) holds FuncLatt (id the carrier of A : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) : ( ( V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V11( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) Function-like one-to-one V17( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) V21( the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) : ( ( ) ( non empty ) set ) ) : ( ( Function-like V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) = id the carrier of (lattice A : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) : ( ( V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) ( non empty V7() V10( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V11( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) Function-like one-to-one V17( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) V21( the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) , the carrier of (lattice b2 : ( ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) ( non empty V71() strict V108(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V109(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V110(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V111(b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) V118() V119() V120() ) VectSp of b1 : ( ( non empty non degenerated V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) ( non empty non degenerated non trivial V71() V91() V97() V99() well-unital distributive V118() V119() V120() ) Field) ) ) : ( ( non empty strict Lattice-like bounded ) ( non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like lower-bounded upper-bounded bounded ) Lattice) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty V7() ) set ) : ( ( ) ( non empty ) set ) ) ;