:: TWOSCOMP semantic presentation

begin

definition
let S be ( ( non empty non void unsplit ) ( non empty non void Circuit-like unsplit ) ManySortedSign ) ;
let A be ( ( V105(S : ( ( non empty non void unsplit ) ( non empty non void Circuit-like unsplit ) ManySortedSign ) ) Boolean ) ( non-empty finitely-generated V105(S : ( ( non empty non void unsplit ) ( non empty non void Circuit-like unsplit ) ManySortedSign ) ) Boolean ) Circuit of S : ( ( non empty non void unsplit ) ( non empty non void Circuit-like unsplit ) ManySortedSign ) ) ;
let s be ( ( ) ( Relation-like Function-like ) State of ) ;
let v be ( ( ) ( ) Vertex of ( ( ) ( ) set ) ) ;
:: original: .
redefine func s . v -> ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func and2 -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 1
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func and2a -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 2
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func and2b -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 3
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func nand2 -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 4
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nand2a -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 5
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nand2b -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 6
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func or2 -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 7
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func or2a -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 8
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func or2b -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 9
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func nor2 -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 10
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nor2a -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 11
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nor2b -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 12
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func xor2 -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 13
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func xor2a -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 14
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func xor2b -> ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 15
 for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

theorem :: TWOSCOMP:1
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( and2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & and2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:2
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( nand2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nand2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nand2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:3
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( or2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & or2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & or2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:4
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( nor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nor2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:5
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( xor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & xor2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = ('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:6
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( and2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nor2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & and2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) ) ;

theorem :: TWOSCOMP:7
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( or2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nand2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & or2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nand2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & or2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nand2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) ) ;

theorem :: TWOSCOMP:8
for x, y being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds xor2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = xor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) ;

theorem :: TWOSCOMP:9
( and2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:10
( or2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or2b : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:11
( xor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor2 : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

definition
func and3 -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 16
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func and3a -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 17
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func and3b -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 18
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func and3c -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 19
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func nand3 -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 20
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nand3a -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 21
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nand3b -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 22
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nand3c -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 23
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func or3 -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 24
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func or3a -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 25
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func or3b -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 26
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func or3c -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 27
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func nor3 -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 28
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nor3a -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 29
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nor3b -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 30
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
func nor3c -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 31
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

definition
func xor3 -> ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) means :: TWOSCOMP:def 32
 for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds it : ( ( non empty ) ( non empty ) ManySortedSign ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( ) set ) = (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ;
end;

theorem :: TWOSCOMP:12
for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:13
for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( nand3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nand3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nand3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nand3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:14
for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = (('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:15
for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( nor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nor3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nor3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & nor3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 'not' ((('not' x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'or' ('not' z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:16
for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nor3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nor3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nor3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) ) ;

theorem :: TWOSCOMP:17
for x, y, z being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) holds
( or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nand3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nand3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nand3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = nand3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*x : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,y : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ,z : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) ) ;

theorem :: TWOSCOMP:18
( and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:19
( and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:20
( and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:21
( and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & and3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:22
( or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:23
( or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3a : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:24
( or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3b : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:25
( or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & or3c : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

theorem :: TWOSCOMP:26
( xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 0 : ( ( ) ( non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) & xor3 : ( ( Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(3 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) = 1 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) ;

begin

definition
let x, b be ( ( ) ( ) set ) ;
func CompStr (x,b) -> ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) equals :: TWOSCOMP:def 33
 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ;
end;

definition
let x, b be ( ( ) ( ) set ) ;
func CompCirc (x,b) -> ( ( strict V105( CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) equals :: TWOSCOMP:def 34
 1GateCircuit (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( strict V105( 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) MSAlgebra over 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) ;
end;

definition
let x, b be ( ( ) ( ) set ) ;
func CompOutput (x,b) -> ( ( ) ( ) Element of InnerVertices (CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) equals :: TWOSCOMP:def 35
[<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) ;
end;

definition
let x, b be ( ( ) ( ) set ) ;
func IncrementStr (x,b) -> ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) equals :: TWOSCOMP:def 36
 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ;
end;

definition
let x, b be ( ( ) ( ) set ) ;
func IncrementCirc (x,b) -> ( ( strict V105( IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) equals :: TWOSCOMP:def 37
 1GateCircuit (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( strict V105( 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) MSAlgebra over 1GateCircStr (<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( non void strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) ;
end;

definition
let x, b be ( ( ) ( ) set ) ;
func IncrementOutput (x,b) -> ( ( ) ( ) Element of InnerVertices (IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) equals :: TWOSCOMP:def 38
[<*x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) ;
end;

definition
let x, b be ( ( ) ( ) set ) ;
func BitCompStr (x,b) -> ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) equals :: TWOSCOMP:def 39
(CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) +* (IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( non empty strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ;
end;

definition
let x, b be ( ( ) ( ) set ) ;
func BitCompCirc (x,b) -> ( ( strict V105( BitCompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) equals :: TWOSCOMP:def 40
(CompCirc (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( strict V105( CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) +* (IncrementCirc (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( strict V105( IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( strict non-empty ) ( strict non-empty finitely-generated V105((CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) +* (IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( non empty strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) MSAlgebra over (CompStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) +* (IncrementStr (x : ( ( non empty ) ( non empty ) ManySortedSign ) ,b : ( ( ) ( ) MSAlgebra over x : ( ( non empty ) ( non empty ) ManySortedSign ) ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( non empty strict ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) ;
end;

theorem :: TWOSCOMP:27
for x, b being ( ( non pair ) ( non pair ) set ) holds the carrier of (CompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) = {x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) } : ( ( ) ( non with_pair ) set ) \/ {[<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) } : ( ( ) ( Relation-like Function-like ) set ) : ( ( ) ( ) set ) ;

theorem :: TWOSCOMP:28
for x, b being ( ( non pair ) ( non pair ) set ) holds [<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) in InnerVertices (CompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:29
for x, b being ( ( non pair ) ( non pair ) set ) holds
( x : ( ( non pair ) ( non pair ) set ) in InputVertices (CompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) & b : ( ( non pair ) ( non pair ) set ) in InputVertices (CompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TWOSCOMP:30
for x, b being ( ( non pair ) ( non pair ) set ) holds InputVertices (CompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) is without_pairs ;

theorem :: TWOSCOMP:31
for x, b being ( ( non pair ) ( non pair ) set ) holds the carrier of (IncrementStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) = {x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) } : ( ( ) ( non with_pair ) set ) \/ {[<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) } : ( ( ) ( Relation-like Function-like ) set ) : ( ( ) ( ) set ) ;

theorem :: TWOSCOMP:32
for x, b being ( ( non pair ) ( non pair ) set ) holds [<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) in InnerVertices (IncrementStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:33
for x, b being ( ( non pair ) ( non pair ) set ) holds
( x : ( ( non pair ) ( non pair ) set ) in InputVertices (IncrementStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) & b : ( ( non pair ) ( non pair ) set ) in InputVertices (IncrementStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TWOSCOMP:34
for x, b being ( ( non pair ) ( non pair ) set ) holds InputVertices (IncrementStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) is without_pairs ;

theorem :: TWOSCOMP:35
for x, b being ( ( non pair ) ( non pair ) set ) holds InnerVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) is ( ( Relation-like ) ( Relation-like ) Relation) ;

theorem :: TWOSCOMP:36
for x, b being ( ( non pair ) ( non pair ) set ) holds
( x : ( ( non pair ) ( non pair ) set ) in the carrier of (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) & b : ( ( non pair ) ( non pair ) set ) in the carrier of (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) & [<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) in the carrier of (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) & [<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) in the carrier of (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:37
for x, b being ( ( non pair ) ( non pair ) set ) holds the carrier of (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) = {x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) } : ( ( ) ( non with_pair ) set ) \/ {[<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) ,[<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) } : ( ( ) ( Relation-like ) set ) : ( ( ) ( ) set ) ;

theorem :: TWOSCOMP:38
for x, b being ( ( non pair ) ( non pair ) set ) holds InnerVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) = {[<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) ,[<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) } : ( ( ) ( Relation-like ) set ) ;

theorem :: TWOSCOMP:39
for x, b being ( ( non pair ) ( non pair ) set ) holds
( [<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) in InnerVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) & [<*x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() nonpair-yielding ) set ) ,and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ] : ( ( ) ( non empty pair ) set ) in InnerVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TWOSCOMP:40
for x, b being ( ( non pair ) ( non pair ) set ) holds InputVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) = {x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) } : ( ( ) ( non with_pair ) set ) ;

theorem :: TWOSCOMP:41
for x, b being ( ( non pair ) ( non pair ) set ) holds
( x : ( ( non pair ) ( non pair ) set ) in InputVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) & b : ( ( non pair ) ( non pair ) set ) in InputVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TWOSCOMP:42
for x, b being ( ( non pair ) ( non pair ) set ) holds InputVertices (BitCompStr (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) Element of K19( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) is without_pairs ;

theorem :: TWOSCOMP:43
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (CompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (CompOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*(s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) ,(s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (CompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (CompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:44
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of )
for a1, a2 being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) st a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (CompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (CompOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = ('not' a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (CompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (CompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:45
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (CompOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*(s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) ,(s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:46
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of )
for a1, a2 being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) st a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (CompOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = ('not' a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:47
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (IncrementCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (IncrementOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*(s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) ,(s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (IncrementCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (IncrementCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:48
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of )
for a1, a2 being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) st a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (IncrementCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (IncrementOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = ('not' a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (IncrementCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (IncrementCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:49
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (IncrementOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*(s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) ,(s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:50
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of )
for a1, a2 being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) st a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (IncrementOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = ('not' a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:51
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (CompOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = xor2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*(s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) ,(s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (IncrementOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = and2a : ( ( Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) ) ( Relation-like 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) -defined BOOLEAN : ( ( ) ( non empty ) set ) -valued Function-like V18(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) boolean-valued ) Function of 2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -tuples_on BOOLEAN : ( ( ) ( non empty ) set ) : ( ( ) ( ) FinSequenceSet of BOOLEAN : ( ( ) ( non empty ) set ) ) , BOOLEAN : ( ( ) ( non empty ) set ) ) . <*(s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) ,(s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) ) : ( ( ) ( ) set ) *> : ( ( ) ( Relation-like K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V34() V41(2 : ( ( ) ( non empty non pair V21() V22() V23() V27() ) Element of K92() : ( ( ) ( non empty V21() V22() V23() V34() V49() V50() ) Element of K19(K88() : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V49() ) set ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) ) ;

theorem :: TWOSCOMP:52
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of )
for a1, a2 being ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) st a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) & a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) = s : ( ( ) ( Relation-like Function-like ) State of ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) holds
( (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (CompOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (CompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = ('not' a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) 'xor' a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . (IncrementOutput (x : ( ( non pair ) ( non pair ) set ) ,b : ( ( non pair ) ( non pair ) set ) )) : ( ( ) ( ) Element of InnerVertices (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( non empty ) Element of K19( the carrier of (IncrementStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = ('not' a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) '&' a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . x : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a1 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) & (Following s : ( ( ) ( Relation-like Function-like ) State of ) ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) . b : ( ( non pair ) ( non pair ) set ) : ( ( ) ( ) set ) = a2 : ( ( ) ( non pair V21() V22() V23() V27() boolean ) Element of BOOLEAN : ( ( ) ( non empty ) set ) ) ) ;

theorem :: TWOSCOMP:53
for x, b being ( ( non pair ) ( non pair ) set )
for s being ( ( ) ( Relation-like Function-like ) State of ) holds Following s : ( ( ) ( Relation-like Function-like ) State of ) : ( ( ) ( Relation-like Function-like ) Element of K216( the Sorts of (BitCompCirc (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( strict V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) ( strict non-empty finitely-generated V105( BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) gate`2=den Boolean ) Circuit of BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) ) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) ) : ( ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like V14( the carrier of (BitCompStr (b1 : ( ( non pair ) ( non pair ) set ) ,b2 : ( ( non pair ) ( non pair ) set ) )) : ( ( non empty non void strict unsplit gate`1=arity gate`2isBoolean ) ( non empty non void strict Circuit-like unsplit gate`1=arity gate`2isBoolean gate`2=den ) ManySortedSign ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( functional V47() V48() ) set ) ) is stable ;