begin
definition
let S be ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ;
let X be ( (
Relation-like the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ;
func Free (
S,
X)
-> ( (
strict ) (
strict )
MSAlgebra over
S : ( ( non
empty ) ( non
empty )
set ) )
means
ex
A being ( ( ) ( non
empty Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
MSSubset of
S : ( ( non
empty ) ( non
empty )
set ) ) st
(
it : ( ( ) (
Relation-like the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) )
Function-yielding V54() )
ManySortedFunction of the
Arity of
S : ( ( non
empty ) ( non
empty )
set ) : ( (
Function-like V25( the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) , the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) )) ) ) (
Relation-like the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ))
-valued Function-like V25( the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) , the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) )) )
Function-yielding V54() )
Element of
bool [: the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ,( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) *) : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
* (X : ( ( ) ( ) set ) #) : ( (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ))
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) )) ) ) ( non
empty Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ))
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) )) ) )
set ) : ( (
Relation-like ) (
Relation-like the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
set ) , the
ResultSort of
S : ( ( non
empty ) ( non
empty )
set ) : ( (
Function-like V25( the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) , the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) (
Relation-like the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-valued Function-like V25( the
carrier' of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) , the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
Element of
bool [: the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
* X : ( ( ) ( )
set ) : ( (
Relation-like ) (
Relation-like )
set ) )
= GenMSAlg A : ( ( ) ( non
empty Relation-like the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
MSSubset of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) : ( (
strict ) (
strict )
MSSubAlgebra of
FreeMSA (X : ( ( ) ( ) set ) \/ ( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
set ) : ( ( ) ( )
MSAlgebra over
S : ( ( non
empty ) ( non
empty )
set ) ) ) &
A : ( ( ) ( non
empty Relation-like the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
MSSubset of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) )
= (Reverse (X : ( ( ) ( ) set ) \/ ( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined Function-like V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined Function-like V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) set ) ) : ( ( ) ( non
empty Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) )
Function-yielding V54() )
ManySortedFunction of
FreeGen (X : ( ( ) ( ) set ) \/ ( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
set ) : ( ( ) ( non
empty Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
GeneratorSet of
FreeMSA (X : ( ( ) ( ) set ) \/ ( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) V25( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
set ) : ( ( ) ( )
MSAlgebra over
S : ( ( non
empty ) ( non
empty )
set ) ) ) ,
X : ( ( ) ( )
set )
\/ ( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( (
Function-like V25( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ,
bool NAT : ( ( ) ( non
empty V17()
V18()
V19() )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like non-empty the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined bool NAT : ( ( ) ( non
empty V17()
V18()
V19() )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty )
set )
-valued Function-like constant V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) )
V25( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ,
bool NAT : ( ( ) ( non
empty V17()
V18()
V19() )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) ) : ( (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
set ) )
"" X : ( ( ) ( )
set ) : ( (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) ) (
Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
set ) );
end;
theorem
for
S being ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature)
for
X being ( (
Relation-like V9() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like V9() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )
for
x being ( ( ) ( )
Element of
(Free (S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ,X : ( ( Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) )) : ( (
strict ) (
strict non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) holds
x : ( ( ) ( )
Element of
(Free (b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ,b2 : ( ( Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) )) : ( (
strict ) (
strict non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) is ( ( ) (
Relation-like the
carrier of
(DTConMSA (b2 : ( ( Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like non-empty non empty-yielding the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like non-empty non empty-yielding the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set )
-valued Function-like finite DecoratedTree-like finite-order finite-branching )
Term of ( ( ) ( non
empty functional constituted-DTrees )
Element of
bool (FinTrees the carrier of (DTConMSA (X : ( ( Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like non-empty non empty-yielding the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like non-empty non empty-yielding the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty functional constituted-DTrees )
DTree-set of the
carrier of
(DTConMSA (b2 : ( ( Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V9() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like non-empty non empty-yielding the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like non-empty non empty-yielding the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty )
set ) ) ,
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ;
definition
let S be ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ;
let Y be ( (
Relation-like V8() the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like V8() non
empty-yielding the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ;
let X be ( (
Relation-like the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ;
func S -Terms (
X,
Y)
-> ( ( ) ( non
empty Relation-like the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set )
-defined Function-like V24( the
carrier of
S : ( ( non
empty ) ( non
empty )
set ) : ( ( ) ( )
set ) ) )
MSSubset of
S : ( ( non
empty ) ( non
empty )
set ) )
means
for
s being ( ( ) ( )
SortSymbol of ( ( ) ( )
set ) ) holds
it : ( (
Function-like V25(
Y : ( ( ) ( )
set ) ,
S : ( ( non
empty ) ( non
empty )
set ) ) ) (
Relation-like Y : ( ( ) ( )
set )
-defined S : ( ( non
empty ) ( non
empty )
set )
-valued Function-like V25(
Y : ( ( ) ( )
set ) ,
S : ( ( non
empty ) ( non
empty )
set ) ) )
Element of
bool [:Y : ( ( ) ( ) set ) ,S : ( ( non empty ) ( non empty ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
. s : ( ( ) ( )
SortSymbol of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
= { t : ( ( ) ( non empty Relation-like the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) -valued Function-like finite DecoratedTree-like finite-order finite-branching ) Term of ( ( ) ( non empty functional constituted-DTrees ) Element of bool (FinTrees the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional constituted-DTrees ) DTree-set of the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ,S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ) where t is ( ( ) ( non empty Relation-like the carrier of (DTConMSA Y : ( ( ) ( ) set ) ) : ( ( ) ( ) DTConstrStr ) : ( ( ) ( ) set ) -valued Function-like finite DecoratedTree-like finite-order finite-branching ) Term of ( ( ) ( functional constituted-DTrees ) Element of bool (FinTrees the carrier of (DTConMSA Y : ( ( ) ( ) set ) ) : ( ( ) ( ) DTConstrStr ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional constituted-DTrees ) DTree-set of the carrier of (DTConMSA Y : ( ( ) ( ) set ) ) : ( ( ) ( ) DTConstrStr ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) ) ,S : ( ( non empty ) ( non empty ) set ) ) : ( the_sort_of t : ( ( ) ( non empty Relation-like the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) -valued Function-like finite DecoratedTree-like finite-order finite-branching ) Term of ( ( ) ( non empty functional constituted-DTrees ) Element of bool (FinTrees the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional constituted-DTrees ) DTree-set of the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ,S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ) : ( ( ) ( ) Element of the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) = s : ( ( ) ( ) SortSymbol of ( ( ) ( non empty ) set ) ) & variables_in t : ( ( ) ( non empty Relation-like the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) -valued Function-like finite DecoratedTree-like finite-order finite-branching ) Term of ( ( ) ( non empty functional constituted-DTrees ) Element of bool (FinTrees the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty functional constituted-DTrees ) DTree-set of the carrier of (DTConMSA Y : ( ( Relation-like V8() the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( non empty Relation-like V8() non empty-yielding the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ,S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ) : ( ( ) ( non empty Relation-like the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined Function-like V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ManySortedSubset of Y : ( ( ) ( ) set ) ) c= X : ( ( ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined Function-like V24( the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) Function-yielding V54() ) ManySortedFunction of the Arity of S : ( ( non empty ) ( non empty ) set ) : ( ( Function-like V25( the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) * : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) ) ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) * : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) -valued Function-like V25( the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) * : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) ) Function-yielding V54() ) Element of bool [: the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ,( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) *) : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) * (Y : ( ( ) ( ) set ) #) : ( ( Relation-like the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) * : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) -defined Function-like V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) * : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) ) ) ( non empty Relation-like the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) * : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) -defined Function-like V24( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) * : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) )) ) ) set ) : ( ( Relation-like ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined Function-like V24( the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) set ) , the ResultSort of S : ( ( non empty ) ( non empty ) set ) : ( ( Function-like V25( the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) ( Relation-like the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -defined the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) -valued Function-like V25( the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) ) ) Element of bool [: the carrier' of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) , the carrier of S : ( ( non empty ) ( non empty ) set ) : ( ( ) ( ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) * Y : ( ( ) ( ) set ) : ( ( Relation-like ) ( Relation-like ) set ) ) ) } ;
end;
theorem
for
S being ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature)
for
X being ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )
for
t being ( ( ) ( non
empty Relation-like the
carrier of
(DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set )
-valued Function-like finite DecoratedTree-like finite-order finite-branching )
Term of ( ( ) ( non
empty functional constituted-DTrees )
Element of
bool (FinTrees the carrier of (DTConMSA (X : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty functional constituted-DTrees )
DTree-set of the
carrier of
(DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty )
set ) ) ,
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) )
for
s being ( ( ) ( )
SortSymbol of ( ( ) ( non
empty )
set ) ) st
t : ( ( ) ( non
empty Relation-like the
carrier of
(DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set )
-valued Function-like finite DecoratedTree-like finite-order finite-branching )
Term of ( ( ) ( non
empty functional constituted-DTrees )
Element of
bool (FinTrees the carrier of (DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty functional constituted-DTrees )
DTree-set of the
carrier of
(DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty )
set ) ) ,
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) )
in (S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) -Terms (X : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ,(X : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) )) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
MSSubset of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) )
. s : ( ( ) ( )
SortSymbol of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) holds
t : ( ( ) ( non
empty Relation-like the
carrier of
(DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set )
-valued Function-like finite DecoratedTree-like finite-order finite-branching )
Term of ( ( ) ( non
empty functional constituted-DTrees )
Element of
bool (FinTrees the carrier of (DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non empty strict with_terminals with_nonterminals with_useful_nonterminals ) DTConstrStr ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty functional constituted-DTrees )
DTree-set of the
carrier of
(DTConMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) ( non
empty strict with_terminals with_nonterminals with_useful_nonterminals )
DTConstrStr ) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( non
empty )
set ) ) ,
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) )
in the
Sorts of
(Free (S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ,X : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) )) : ( (
strict ) (
strict )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set )
. s : ( ( ) ( )
SortSymbol of ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ;
theorem
for
S being ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature)
for
X being ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) holds
(FreeMSA (X : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) )
| (S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) -Terms (X : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ,(X : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of S : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) )) : ( ( ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
MSSubset of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) : ( (
strict ) (
strict )
MSSubAlgebra of
FreeMSA (b2 : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) \/ ( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) --> {0 : ( ( ) ( empty Relation-like non-empty empty-yielding NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined Function-like one-to-one constant functional V17() V18() V19() V21() V22() V23() finite FinSequence-like FinSubsequence-like FinSequence-membered constituted-Trees constituted-FinTrees constituted-DTrees Tree-yielding FinTree-yielding DTree-yielding Function-yielding V54() V163() V164() ext-real ) Element of NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) } : ( ( ) ( non empty functional ) Element of bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) : ( ( Function-like V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) ( Relation-like non-empty the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) -valued Function-like constant V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) V25( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) ) ) Element of bool [: the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,(bool NAT : ( ( ) ( non empty V17() V18() V19() ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( non empty ) set ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like non-empty the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) )
= Free (
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ,
X : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) : ( (
strict ) (
strict )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ;
theorem
for
S being ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature)
for
X,
Y being ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
S : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )
for
A being ( ( ) ( )
MSSubAlgebra of
FreeMSA X : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) )
for
B being ( ( ) ( )
MSSubAlgebra of
FreeMSA Y : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) st the
Sorts of
A : ( ( ) ( )
MSSubAlgebra of
FreeMSA b2 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set )
= the
Sorts of
B : ( ( ) ( )
MSSubAlgebra of
FreeMSA b3 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) holds
MSAlgebra(# the
Sorts of
A : ( ( ) ( )
MSSubAlgebra of
FreeMSA b2 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) , the
Charact of
A : ( ( ) ( )
MSSubAlgebra of
FreeMSA b2 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )
Function-yielding V54() )
ManySortedFunction of the
Arity of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( (
Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) )
Function-yielding V54() )
Element of
bool [: the carrier' of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) )) :] : ( ( ) ( non
empty Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
* ( the Sorts of b4 : ( ( ) ( ) MSSubAlgebra of FreeMSA b2 : ( ( Relation-like V8() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like V8() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) : ( ( ) ( strict non-empty free feasible non empty ) MSAlgebra over b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) #) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
set ) : ( (
Relation-like ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) , the
ResultSort of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( (
Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier' of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
* the
Sorts of
b4 : ( ( ) ( )
MSSubAlgebra of
FreeMSA b2 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) : ( (
Relation-like ) (
Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like )
set ) ) #) : ( (
strict ) (
strict )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) )
= MSAlgebra(# the
Sorts of
B : ( ( ) ( )
MSSubAlgebra of
FreeMSA b3 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) , the
Charact of
B : ( ( ) ( )
MSSubAlgebra of
FreeMSA b3 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( ( ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )
Function-yielding V54() )
ManySortedFunction of the
Arity of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( (
Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) (
Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ))
-valued Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) )
Function-yielding V54() )
Element of
bool [: the carrier' of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ,( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) *) : ( ( ) ( non empty functional FinSequence-membered ) M8( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) )) :] : ( ( ) ( non
empty Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
* ( the Sorts of b5 : ( ( ) ( ) MSSubAlgebra of FreeMSA b3 : ( ( Relation-like V8() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like V8() the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ManySortedSet of the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) : ( ( ) ( strict non-empty free feasible non empty ) MSAlgebra over b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) ) ) : ( ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) ( Relation-like the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) -defined Function-like V24( the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) ) ) set ) #) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) ) ) ( non
empty Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ))
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
* : ( ( ) ( non
empty functional FinSequence-membered )
M8( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) )) ) )
set ) : ( (
Relation-like ) ( non
empty Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) , the
ResultSort of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( (
Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-valued Function-like V25( the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) , the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
Element of
bool [: the carrier' of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) , the carrier of b1 : ( ( non void V159() ) ( non empty non void feasible V159() ) Signature) : ( ( ) ( non empty ) set ) :] : ( ( ) (
Relation-like )
set ) : ( ( ) ( non
empty )
set ) )
* the
Sorts of
b5 : ( ( ) ( )
MSSubAlgebra of
FreeMSA b3 : ( (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like V8() the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
ManySortedSet of the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) : ( ( ) (
strict non-empty free feasible non
empty )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ) : ( (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) ) (
Relation-like the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like V24( the
carrier of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set ) ) )
set ) : ( (
Relation-like ) (
Relation-like the
carrier' of
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) : ( ( ) ( non
empty )
set )
-defined Function-like )
set ) ) #) : ( (
strict ) (
strict )
MSAlgebra over
b1 : ( ( non
void V159() ) ( non
empty non
void feasible V159() )
Signature) ) ;