begin
definition
let V be ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) ;
mode Subspace of
V -> ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace)
means
( the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set )
c= the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set ) &
0. it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
Element of the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set ) )
= 0. V : ( ( ) ( )
UNITSTR ) : ( ( ) (
V55(
V : ( ( ) ( )
UNITSTR ) ) )
Element of the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set ) ) & the
addF of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( (
Function-like V18(
[: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set ) ) ) (
Relation-like [: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set )
-defined the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set )
-valued Function-like V18(
[: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set ) ) )
Element of
bool [:[: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
= the
addF of
V : ( ( ) ( )
UNITSTR ) : ( (
Function-like V18(
[: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set ) ) ) (
Relation-like [: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set )
-defined the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set )
-valued Function-like V18(
[: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set ) ) )
Element of
bool [:[: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
|| the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set ) : ( ( ) (
Relation-like Function-like )
set ) & the
Mult of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( (
Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set ) ) ) (
Relation-like [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set )
-defined the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set )
-valued Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set ) ) )
Element of
bool [:[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
= the
Mult of
V : ( ( ) ( )
UNITSTR ) : ( (
Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set ) ) ) (
Relation-like [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set )
-defined the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set )
-valued Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) , the
carrier of
V : ( ( ) ( )
UNITSTR ) : ( ( ) ( )
set ) ) )
Element of
bool [:[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
| [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) : ( (
Relation-like ) (
Relation-like Function-like )
set ) & the
scalar of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( (
Function-like V18(
[: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) ) (
Relation-like [: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set )
-defined REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set )
-valued Function-like V18(
[: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
V119()
V120()
V121() )
Element of
bool [:[: the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) , the carrier of it : ( ( ) ( ) Element of V : ( ( ) ( ) UNITSTR ) ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) ,REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) :] : ( ( ) (
V119()
V120()
V121() )
set ) : ( ( ) ( non
empty )
set ) )
= the
scalar of
V : ( ( ) ( )
UNITSTR ) : ( (
Function-like V18(
[: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) ) (
Relation-like [: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set )
-defined REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set )
-valued Function-like V18(
[: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
V119()
V120()
V121() )
Element of
bool [:[: the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) , the carrier of V : ( ( ) ( ) UNITSTR ) : ( ( ) ( ) set ) :] : ( ( ) ( ) set ) ,REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) :] : ( ( ) (
V119()
V120()
V121() )
set ) : ( ( ) ( non
empty )
set ) )
|| the
carrier of
it : ( ( ) ( )
Element of
V : ( ( ) ( )
UNITSTR ) ) : ( ( ) ( )
set ) : ( ( ) (
Relation-like Function-like )
set ) );
end;
theorem
for
V being ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace)
for
V1 being ( ( ) ( )
Subset of )
for
D being ( ( non
empty ) ( non
empty )
set )
for
d1 being ( ( ) ( )
Element of
D : ( ( non
empty ) ( non
empty )
set ) )
for
A being ( (
Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like [:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
BinOp of
D : ( ( non
empty ) ( non
empty )
set ) )
for
M being ( (
Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,D : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
D : ( ( non
empty ) ( non
empty )
set ) )
for
S being ( (
Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) ) (
Relation-like [:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set )
-valued Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
V119()
V120()
V121() )
Function of
[:D : ( ( non empty ) ( non empty ) set ) ,D : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) st
V1 : ( ( ) ( )
Subset of )
= D : ( ( non
empty ) ( non
empty )
set ) &
d1 : ( ( ) ( )
Element of
b3 : ( ( non
empty ) ( non
empty )
set ) )
= 0. V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) (
V55(
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) )
right_complementable )
Element of the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) ( non
empty )
set ) ) &
A : ( (
Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like [:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
BinOp of
b3 : ( ( non
empty ) ( non
empty )
set ) )
= the
addF of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( (
Function-like V18(
[: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) ( non
empty )
set )
-valued Function-like V18(
[: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [:[: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
|| V1 : ( ( ) ( )
Subset of ) : ( ( ) (
Relation-like Function-like )
set ) &
M : ( (
Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
= the
Mult of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( (
Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) ( non
empty )
set )
-valued Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [:[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
| [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,V1 : ( ( ) ( ) Subset of ) :] : ( ( ) ( )
set ) : ( (
Relation-like ) (
Relation-like Function-like )
set ) &
S : ( (
Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) ) (
Relation-like [:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set )
-valued Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
V119()
V120()
V121() )
Function of
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
= the
scalar of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) : ( (
Function-like V18(
[: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) ) (
Relation-like [: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set )
-valued Function-like V18(
[: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
V119()
V120()
V121() )
Element of
bool [:[: the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) RealUnitarySpace) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty ) set ) ,REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) :] : ( ( ) ( non
empty V119()
V120()
V121() )
set ) : ( ( ) ( non
empty )
set ) )
|| V1 : ( ( ) ( )
Subset of ) : ( ( ) (
Relation-like Function-like )
set ) holds
UNITSTR(#
D : ( ( non
empty ) ( non
empty )
set ) ,
d1 : ( ( ) ( )
Element of
b3 : ( ( non
empty ) ( non
empty )
set ) ) ,
A : ( (
Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like [:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
BinOp of
b3 : ( ( non
empty ) ( non
empty )
set ) ) ,
M : ( (
Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ,
S : ( (
Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) ) (
Relation-like [:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set )
-valued Function-like V18(
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
V119()
V120()
V121() )
Function of
[:b3 : ( ( non empty ) ( non empty ) set ) ,b3 : ( ( non empty ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) #) : ( (
strict ) ( non
empty strict )
UNITSTR ) is ( ( ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
Subspace of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) ) ;
begin
definition
let V be ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
RealUnitarySpace) ;
func (Omega). V -> ( (
strict ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like )
Subspace of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) )
equals
UNITSTR(# the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set ) , the
ZeroF of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) (
right_complementable )
Element of the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set ) ) , the
addF of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( (
Function-like V18(
[: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like [: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set )
-valued Function-like V18(
[: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [:[: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) , the
Mult of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( (
Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like [:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set )
-valued Function-like V18(
[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) , the
carrier of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [:[:REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) , the
scalar of
V : ( ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non
empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like )
UNITSTR ) : ( (
Function-like V18(
[: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) ) ) (
Relation-like [: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set )
-defined REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set )
-valued Function-like V18(
[: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non
empty )
set ) ,
REAL : ( ( ) ( non
empty V36()
V129()
V130()
V131()
V135() )
set ) )
V119()
V120()
V121() )
Element of
bool [:[: the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) , the carrier of V : ( ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) ( non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RealUnitarySpace-like ) UNITSTR ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty ) set ) ,REAL : ( ( ) ( non empty V36() V129() V130() V131() V135() ) set ) :] : ( ( ) ( non
empty V119()
V120()
V121() )
set ) : ( ( ) ( non
empty )
set ) ) #) : ( (
strict ) ( non
empty strict )
UNITSTR ) ;
end;
begin
begin
begin