begin
theorem
for
X1,
Y1,
X2,
Y2 being ( ( non
empty ) ( non
empty )
set )
for
f being ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
X1 : ( ( non
empty ) ( non
empty )
set ) ,
X2 : ( ( non
empty ) ( non
empty )
set ) )
for
g being ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
-defined b4 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
Y1 : ( ( non
empty ) ( non
empty )
set ) ,
Y2 : ( ( non
empty ) ( non
empty )
set ) ) st
f : ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
c= g : ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
-defined b4 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) holds
f : ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
* : ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) )) ,
b3 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) )) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) ))
-defined b3 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) )) ,
b3 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) )) ) )
Element of
K19(
K20(
(b1 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) )) ,
(b3 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
c= g : ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
-defined b4 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) )
* : ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) )) ,
b4 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) )) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) ))
-defined b4 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) )) ,
b4 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) )) ) )
Element of
K19(
K20(
(b2 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) )) ,
(b4 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
X1,
Y1,
X2,
Y2 being ( ( non
empty ) ( non
empty )
set )
for
f being ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
X1 : ( ( non
empty ) ( non
empty )
set ) ,
X2 : ( ( non
empty ) ( non
empty )
set ) )
for
g being ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
-defined b4 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
Y1 : ( ( non
empty ) ( non
empty )
set ) ,
Y2 : ( ( non
empty ) ( non
empty )
set ) ) st
f : ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
tolerates g : ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
-defined b4 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) holds
f : ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
-defined b3 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b1 : ( ( non
empty ) ( non
empty )
set ) ,
b3 : ( ( non
empty ) ( non
empty )
set ) )
* : ( (
Function-like V18(
b1 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) )) ,
b3 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) )) ) ) (
Relation-like b1 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) ))
-defined b3 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18(
b1 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) )) ,
b3 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) )) ) )
Element of
K19(
K20(
(b1 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b1 : ( ( non
empty ) ( non
empty )
set ) )) ,
(b3 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b3 : ( ( non
empty ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
tolerates g : ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
-defined b4 : ( ( non
empty ) ( non
empty )
set )
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) ) )
Function of
b2 : ( ( non
empty ) ( non
empty )
set ) ,
b4 : ( ( non
empty ) ( non
empty )
set ) )
* : ( (
Function-like V18(
b2 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) )) ,
b4 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) )) ) ) (
Relation-like b2 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) ))
-defined b4 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18(
b2 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) )) ,
b4 : ( ( non
empty ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) )) ) )
Element of
K19(
K20(
(b2 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b2 : ( ( non
empty ) ( non
empty )
set ) )) ,
(b4 : ( ( non empty ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
b4 : ( ( non
empty ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) ;
begin
definition
let S be ( ( non
empty non
void ) ( non
empty non
void feasible feasible )
ManySortedSign ) ;
let f,
g be ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) ;
pred f,
g form_a_replacement_in S means
for
o1,
o2 being ( ( ) ( )
OperSymbol of ( ( ) ( )
set ) ) st
((id the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( total ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -valued Function-like one-to-one total V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ) ) Element of K19(K20( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) +* g : ( ( ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like total V53() ) ManySortedFunction of the Arity of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( Function-like V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) -valued Function-like total V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) ) Element of K19(K20( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ,( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) * (f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) #) : ( ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) -defined Function-like total ) ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) -defined Function-like non empty total ) set ) : ( ( Relation-like ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like total ) set ) , the ResultSort of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( Function-like V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -valued Function-like total V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) Element of K19(K20( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) * f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) : ( ( Relation-like ) ( Relation-like ) set ) ) ) : ( (
Relation-like Function-like ) (
Relation-like the
carrier' of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( )
set )
\/ the
carrier' of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( )
set )
-defined Function-like total total )
set )
. o1 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
= ((id the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( total ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -valued Function-like one-to-one total V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ) ) Element of K19(K20( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) +* g : ( ( ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like total V53() ) ManySortedFunction of the Arity of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( Function-like V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) -valued Function-like total V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) ) Element of K19(K20( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) ,( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) * (f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) #) : ( ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) -defined Function-like total ) ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) -defined Function-like non empty total ) set ) : ( ( Relation-like ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined Function-like total ) set ) , the ResultSort of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( Function-like V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -valued Function-like total V18( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) Element of K19(K20( the carrier' of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) * f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) : ( ( Relation-like ) ( Relation-like ) set ) ) ) : ( (
Relation-like Function-like ) (
Relation-like the
carrier' of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( )
set )
\/ the
carrier' of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined the
carrier' of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( )
set )
-defined Function-like total total )
set )
. o2 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) holds
(
((id the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( total ) ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -valued Function-like one-to-one non empty total V18( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) Element of K19(K20( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) +* f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) ) : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
* (the_arity_of o1 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
-valued Function-like V31()
FinSequence-like FinSubsequence-like )
Element of the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )) ) : ( (
Relation-like ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined Function-like )
set )
= ((id the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( total ) ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -valued Function-like one-to-one non empty total V18( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) Element of K19(K20( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) +* f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) ) : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
* (the_arity_of o2 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
-valued Function-like V31()
FinSequence-like FinSubsequence-like )
Element of the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )) ) : ( (
Relation-like ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined Function-like )
set ) &
((id the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( total ) ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -valued Function-like one-to-one non empty total V18( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) Element of K19(K20( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) +* f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) ) : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
. (the_result_sort_of o1 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
= ((id the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( total ) ( Relation-like the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -defined the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -valued Function-like one-to-one non empty total V18( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) Element of K19(K20( the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) , the carrier of S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) +* f : ( ( ) ( ) MSAlgebra over S : ( ( non empty ) ( non empty feasible feasible ) ManySortedSign ) ) ) : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
. (the_result_sort_of o2 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) );
end;
definition
let S be ( ( non
empty non
void ) ( non
empty non
void feasible feasible )
ManySortedSign ) ;
let f,
g be ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) ;
assume
f : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) ,
g : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
form_a_replacement_in S : ( ( non
empty non
void ) ( non
empty non
void feasible feasible )
ManySortedSign )
;
func S with-replacement (
f,
g)
-> ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign )
means
( the
carrier of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-indexing f : ( ( ) ( )
set ) : ( (
Relation-like the
carrier of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total ) (
Relation-like the
carrier of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total )
ManySortedSet of the
carrier of
S : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) , the
carrier' of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-indexing g : ( (
Function-like V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
S : ( ( ) ( )
set ) )) ) ) (
Relation-like f : ( ( ) ( )
set )
-defined S : ( ( ) ( )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
S : ( ( ) ( )
set ) ))
-valued Function-like non
empty total V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11(
S : ( ( ) ( )
set ) )) ) )
Element of
K19(
K20(
f : ( ( ) ( )
set ) ,
(S : ( ( ) ( ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11(
S : ( ( ) ( )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) : ( (
Relation-like the
carrier' of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total ) (
Relation-like the
carrier' of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total )
ManySortedSet of the
carrier' of
S : ( ( ) ( )
set ) : ( ( ) ( )
set ) )
form_morphism_between S : ( ( ) ( )
set ) ,
it : ( (
Function-like V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) ) (
Relation-like f : ( ( ) ( )
set )
-defined S : ( ( ) ( )
set )
-valued Function-like V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) )
Element of
K19(
K20(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) & the
carrier of
it : ( (
Function-like V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) ) (
Relation-like f : ( ( ) ( )
set )
-defined S : ( ( ) ( )
set )
-valued Function-like V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) )
Element of
K19(
K20(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set )
= rng ( the carrier of S : ( ( ) ( ) set ) : ( ( ) ( ) set ) -indexing f : ( ( ) ( ) set ) ) : ( (
Relation-like the
carrier of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total ) (
Relation-like the
carrier of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total )
ManySortedSet of the
carrier of
S : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) & the
carrier' of
it : ( (
Function-like V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) ) (
Relation-like f : ( ( ) ( )
set )
-defined S : ( ( ) ( )
set )
-valued Function-like V18(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) )
Element of
K19(
K20(
f : ( ( ) ( )
set ) ,
S : ( ( ) ( )
set ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set )
= rng ( the carrier' of S : ( ( ) ( ) set ) : ( ( ) ( ) set ) -indexing g : ( ( Function-like V18(f : ( ( ) ( ) set ) ,S : ( ( ) ( ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11(S : ( ( ) ( ) set ) )) ) ) ( Relation-like f : ( ( ) ( ) set ) -defined S : ( ( ) ( ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11(S : ( ( ) ( ) set ) )) -valued Function-like non empty total V18(f : ( ( ) ( ) set ) ,S : ( ( ) ( ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11(S : ( ( ) ( ) set ) )) ) ) Element of K19(K20(f : ( ( ) ( ) set ) ,(S : ( ( ) ( ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) M11(S : ( ( ) ( ) set ) )) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Relation-like the
carrier' of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total ) (
Relation-like the
carrier' of
S : ( ( ) ( )
set ) : ( ( ) ( )
set )
-defined Function-like total )
ManySortedSet of the
carrier' of
S : ( ( ) ( )
set ) : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) );
end;
theorem
for
S1,
S2 being ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature)
for
f being ( (
Function-like V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) )
Function of the
carrier of
S1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
S2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )
for
g being ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) st
f : ( (
Function-like V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) )
Function of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ,
g : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
form_morphism_between S1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) ,
S2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) holds
(f : ( ( Function-like V18( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -valued Function-like non empty total V18( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ) *) : ( (
Function-like V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20(
( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ,
( the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
* the
Arity of
S1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ,
( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) : ( (
Function-like ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ,
( the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
= the
Arity of
S2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ,
( the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
* g : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like ) (
Relation-like the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like )
set ) ;
theorem
for
S being ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature)
for
f,
g being ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) st
f : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) ,
g : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
form_a_replacement_in S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) holds
for
f9 being ( (
Function-like V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) )
Function of the
carrier of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
(S : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (f : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,g : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) st
f9 : ( (
Function-like V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) )
Function of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )
= the
carrier of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-indexing f : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
ManySortedSet of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) holds
for
g9 being ( ( ) (
Relation-like Function-like )
rng-retract of the
carrier' of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-indexing g : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
ManySortedSet of the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) holds the
Arity of
(S : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (f : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,g : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( (
Function-like V18( the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ,
( the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
= ((f9 : ( ( Function-like V18( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total V18( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) ) Function of the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) ) *) : ( ( Function-like V18( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) , the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) ) ( Relation-like the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) -defined the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) -valued Function-like non empty total V18( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) , the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) ) Element of K19(K20(( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) ,( the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) * the Arity of S : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( Function-like V18( the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) ) ) ( Relation-like the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) -valued Function-like non empty total V18( the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) * : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) ) ) Element of K19(K20( the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ,( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) M11( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Function-like ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ,
( the carrier of (b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non empty non void strict ) ( non empty non void feasible strict feasible ) ManySortedSign ) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
* g9 : ( ( ) (
Relation-like Function-like )
rng-retract of the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-indexing b3 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
ManySortedSet of the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) : ( (
Relation-like ) (
Relation-like the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ))
-valued Function-like )
set ) ;
theorem
for
S being ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature)
for
f,
g being ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) st
f : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) ,
g : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
form_a_replacement_in S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) holds
for
g9 being ( ( ) (
Relation-like Function-like )
rng-retract of the
carrier' of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-indexing g : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
ManySortedSet of the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) holds the
ResultSort of
(S : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (f : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,g : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( (
Function-like V18( the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
-defined the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) )
Element of
K19(
K20( the
carrier' of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) , the
carrier of
(b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) with-replacement (b2 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ,b3 : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) )) : ( ( non
empty non
void strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
= (( the carrier of S : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -indexing f : ( ( Relation-like Function-like ) ( Relation-like Function-like ) Function) ) : ( ( Relation-like the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like total ) ( Relation-like the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like non empty total ) ManySortedSet of the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ) * the ResultSort of S : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( Function-like V18( the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -valued Function-like non empty total V18( the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ) ) Element of K19(K20( the carrier' of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like ) set ) ) : ( ( ) ( ) set ) ) ) : ( (
Relation-like ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
set )
* g9 : ( ( ) (
Relation-like Function-like )
rng-retract of the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-indexing b3 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
ManySortedSet of the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) : ( (
Relation-like ) (
Relation-like Function-like )
set ) ;
begin
theorem
for
S1,
S2,
S being ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign )
for
f1,
g1,
f2,
g2 being ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) st
f1 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
tolerates f2 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) &
f1 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) ,
g1 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
form_morphism_between S1 : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) ,
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) &
f2 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) ,
g2 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
form_morphism_between S2 : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) ,
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) holds
f1 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
+* f2 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set ) ,
g1 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function)
+* g2 : ( (
Relation-like Function-like ) (
Relation-like Function-like )
Function) : ( (
Relation-like Function-like ) (
Relation-like Function-like )
set )
form_morphism_between S1 : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign )
+* S2 : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) : ( ( non
empty strict ) ( non
empty feasible strict feasible )
ManySortedSign ) ,
S : ( ( non
empty ) ( non
empty feasible feasible )
ManySortedSign ) ;
begin
theorem
for
S being ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature)
for
E being ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature)
for
A being ( ( ) ( )
MSAlgebra over
E : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) st
A : ( ( ) ( )
MSAlgebra over
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) is ( ( ) ( )
Algebra of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) ) holds
for
o being ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) holds the
Charact of
A : ( ( ) ( )
MSAlgebra over
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) : ( ( ) (
Relation-like the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set )
-defined Function-like total V53() )
ManySortedFunction of the
Arity of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set )
-defined the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like total V18( the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set ) ,
( the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
* ( the Sorts of b3 : ( ( ) ( ) MSAlgebra over b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) ) : ( ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like total ) ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like non
empty total )
set ) : ( (
Relation-like ) (
Relation-like the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set )
-defined Function-like total )
set ) , the
ResultSort of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set )
-defined the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like total V18( the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) )
Element of
K19(
K20( the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set ) , the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
* the
Sorts of
b3 : ( ( ) ( )
MSAlgebra over
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
set ) : ( (
Relation-like ) (
Relation-like the
carrier' of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( )
set )
-defined Function-like total )
set ) )
. o : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) is ( (
Function-like V18(
( the Sorts of b3 : ( ( ) ( ) MSAlgebra over b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) ) : ( ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like total ) ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like non
empty total )
set )
. (the_arity_of b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like V31()
FinSequence-like FinSubsequence-like )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) ( )
set ) , the
Sorts of
b3 : ( ( ) ( )
MSAlgebra over
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
set )
. (the_result_sort_of b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) ) (
Relation-like ( the Sorts of b3 : ( ( ) ( ) MSAlgebra over b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) ) : ( ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like total ) ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like non
empty total )
set )
. (the_arity_of b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like V31()
FinSequence-like FinSubsequence-like )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) ( )
set )
-defined the
Sorts of
b3 : ( ( ) ( )
MSAlgebra over
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
set )
. (the_result_sort_of b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like V18(
( the Sorts of b3 : ( ( ) ( ) MSAlgebra over b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) ) : ( ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like total ) ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like non
empty total )
set )
. (the_arity_of b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like V31()
FinSequence-like FinSubsequence-like )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) ( )
set ) , the
Sorts of
b3 : ( ( ) ( )
MSAlgebra over
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
set )
. (the_result_sort_of b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) )
Function of
( the Sorts of A : ( ( ) ( ) MSAlgebra over b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) ) : ( ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like total ) ( Relation-like the carrier of b2 : ( ( non empty feasible ) ( non empty feasible feasible ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like non
empty total )
set )
. (the_arity_of o : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) (
Relation-like K97() : ( ( ) ( )
Element of
K19(
K93() : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like V31()
FinSequence-like FinSubsequence-like )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) ( )
set ) , the
Sorts of
A : ( ( ) ( )
MSAlgebra over
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) ) : ( (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like total ) (
Relation-like the
carrier of
b2 : ( ( non
empty feasible ) ( non
empty feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like non
empty total )
set )
. (the_result_sort_of o : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( )
Element of the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) ;
theorem
for
S,
S9 being ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature)
for
A being ( (
non-empty disjoint_valued ) (
non-empty disjoint_valued feasible non
empty )
MSAlgebra over
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) ) st
A : ( (
non-empty disjoint_valued ) (
non-empty disjoint_valued feasible non
empty )
MSAlgebra over
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) ) is ( ( ) ( )
MSAlgebra over
S9 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) ) holds
ManySortedSign(# the
carrier of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier' of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
Arity of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ,
( the carrier of b1 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) , the
ResultSort of
S : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) )
Element of
K19(
K20( the
carrier' of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) #) : ( (
strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign )
= ManySortedSign(# the
carrier of
S9 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier' of
S9 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
Arity of
S9 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like non
empty total V18( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
Element of
K19(
K20( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ,
( the carrier of b2 : ( ( non void feasible ) ( non empty non void feasible feasible ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
M11( the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) )) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) , the
ResultSort of
S9 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( (
Function-like V18( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like non
empty total V18( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) )
Element of
K19(
K20( the
carrier' of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b2 : ( ( non
void feasible ) ( non
empty non
void feasible feasible )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) #) : ( (
strict ) ( non
empty non
void feasible strict feasible )
ManySortedSign ) ;