begin
begin
theorem
for
U1,
U2 being ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) st
U1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) is ( ( ) ( non
empty partial quasi_total non-empty )
SubAlgebra of
U2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) ) holds
for
B being ( ( ) (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
MSSubset of
(MSSign U2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) st
B : ( ( ) (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
MSSubset of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) )
= the
Sorts of
(MSAlg U1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) : ( (
Relation-like the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
set ) holds
for
o being ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) )
for
a being ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) st
a : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) )
= o : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) holds
Den (
a : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg U1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( (
Function-like quasi_total ) (
Relation-like Args (
b5 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) )
-defined Result (
b5 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( ( ) ( non
empty )
Element of
rng the
Sorts of
(MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) : ( (
Relation-like the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) )
-valued Function-like quasi_total )
Element of
K19(
K20(
(Args (b5 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) ) ,
(Result (b5 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( ( ) ( non
empty )
Element of
rng the
Sorts of
(MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) : ( (
Relation-like the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
= (Den (o : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg U2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( (
Function-like quasi_total ) (
Relation-like Args (
b4 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) )
-defined Result (
b4 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( ( ) ( non
empty )
Element of
rng the
Sorts of
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) )
-valued Function-like quasi_total )
Element of
K19(
K20(
(Args (b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) ) ,
(Result (b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( ( ) ( non
empty )
Element of
rng the
Sorts of
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) )
| (Args (a : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg U1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) ) : ( (
Function-like ) (
Relation-like Args (
b5 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b1 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b1 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) )
-defined Args (
b4 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) )
-defined Result (
b4 : ( ( ) ( )
OperSymbol of ( ( ) ( non
empty )
set ) ) ,
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) ) : ( ( ) ( non
empty )
Element of
rng the
Sorts of
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) )
-valued Function-like )
Element of
K19(
K20(
(Args (b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( ( ) ( non
empty )
Element of
rng ( the Sorts of (MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) : ( ( Relation-like the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like total ) ( Relation-like non-empty non empty-yielding the carrier of (MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) : ( ( ) ( non empty trivial V33() ) set ) -defined Function-like non empty total ) set ) #) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
* : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set ) )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) ) ,
(Result (b4 : ( ( ) ( ) OperSymbol of ( ( ) ( non empty ) set ) ) ,(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( ( strict ) ( strict non-empty ) MSAlgebra over MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) : ( ( trivial non void strict segmental ) ( non empty trivial V64() non void 1 : ( ( ) ( non empty V26() V27() V28() V32() ) Element of NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) -element V70() strict segmental ) ManySortedSign ) ) )) : ( ( ) ( non
empty )
Element of
rng the
Sorts of
(MSAlg b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign b2 : ( ( non
empty partial quasi_total non-empty ) ( non
empty partial quasi_total non-empty )
Universal_Algebra) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) ) : ( (
Relation-like the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like total ) (
Relation-like non-empty non
empty-yielding the
carrier of
(MSSign b2 : ( ( non empty partial quasi_total non-empty ) ( non empty partial quasi_total non-empty ) Universal_Algebra) ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental )
ManySortedSign ) : ( ( ) ( non
empty trivial V33() )
set )
-defined Function-like non
empty total )
set ) : ( ( ) ( non
empty V45() )
set ) ) ) : ( ( ) (
Relation-like )
set ) ) : ( ( ) ( )
set ) ) ;
begin
theorem
for
A being ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) holds
UnSubAlLattice UAStr(# the
carrier of
A : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) , the
charact of
A : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) (
Relation-like non-empty NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined PFuncs (
( the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) , the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like non
empty Function-yielding V25()
V33()
FinSequence-like FinSubsequence-like homogeneous quasi_total )
FinSequence of
PFuncs (
( the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) , the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) #) : ( (
strict ) ( non
empty strict partial quasi_total non-empty with_const_op )
UAStr ) : ( ( non
empty strict Lattice-like ) ( non
empty strict Lattice-like )
LattStr ) ,
MSSubAlLattice (MSAlg UAStr(# the carrier of A : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) , the charact of A : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( Relation-like non-empty NAT : ( ( ) ( non empty V26() V27() V28() ) Element of K19(REAL : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) -defined PFuncs (( the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) FinSequenceSet of the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) ) , the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) -valued Function-like non empty Function-yielding V25() V33() FinSequence-like FinSubsequence-like homogeneous quasi_total ) FinSequence of PFuncs (( the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) *) : ( ( ) ( functional non empty FinSequence-membered ) FinSequenceSet of the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) ) , the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) #) : ( ( strict ) ( non empty strict partial quasi_total non-empty with_const_op ) UAStr ) ) : ( (
strict ) (
strict non-empty )
MSAlgebra over
MSSign UAStr(# the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) , the
charact of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) (
Relation-like non-empty NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) )
-defined PFuncs (
( the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) , the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set )
-valued Function-like non
empty Function-yielding V25()
V33()
FinSequence-like FinSubsequence-like homogeneous quasi_total )
FinSequence of
PFuncs (
( the carrier of b1 : ( ( non empty partial quasi_total non-empty with_const_op ) ( non empty partial quasi_total non-empty with_const_op ) Universal_Algebra) : ( ( ) ( non empty ) set ) *) : ( ( ) (
functional non
empty FinSequence-membered )
FinSequenceSet of the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) , the
carrier of
b1 : ( ( non
empty partial quasi_total non-empty with_const_op ) ( non
empty partial quasi_total non-empty with_const_op )
Universal_Algebra) : ( ( ) ( non
empty )
set ) ) : ( ( ) ( )
set ) ) #) : ( (
strict ) ( non
empty strict partial quasi_total non-empty with_const_op )
UAStr ) : ( (
trivial non
void strict segmental ) ( non
empty trivial V64() non
void 1 : ( ( ) ( non
empty V26()
V27()
V28()
V32() )
Element of
NAT : ( ( ) ( non
empty V26()
V27()
V28() )
Element of
K19(
REAL : ( ( ) ( )
set ) ) : ( ( ) ( )
set ) ) )
-element V70()
strict segmental all-with_const_op )
ManySortedSign ) ) : ( ( non
empty strict Lattice-like ) ( non
empty strict Lattice-like V86() )
LattStr )
are_isomorphic ;