:: MSUALG_6 semantic presentation

REAL is set

NAT is non empty V4() V5() V6() V35() V40() V41() Element of bool REAL

bool REAL is set

COMPLEX is set

NAT is non empty V4() V5() V6() V35() V40() V41() set

bool NAT is V35() set

bool NAT is V35() set

[:NAT,NAT:] is Relation-like V35() set

[:[:NAT,NAT:],NAT:] is Relation-like V35() set

bool [:[:NAT,NAT:],NAT:] is V35() set

K281() is non empty V80() L9()

the carrier of K281() is non empty set

K284() is Element of bool NAT

[:K284(),K284():] is Relation-like set

[:[:K284(),K284():],K284():] is Relation-like set

bool [:[:K284(),K284():],K284():] is set

{} is empty V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V32() V35() V40() V42( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete Function-yielding Relation-yielding FuncSeq-like irreflexive set

1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

2 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

3 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

Seg 1 is non empty trivial V35() V42(1) Element of bool NAT

{1} is non empty trivial V42(1) set

Seg 2 is non empty V35() V42(2) Element of bool NAT

{1,2} is non empty set

0 is empty V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V32() V35() V40() V42( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete Function-yielding Relation-yielding FuncSeq-like irreflexive Element of NAT

S is non empty feasible ManySortedSign

the carrier of S is non empty set

S is set

A is Relation-like S -defined Function-like total set

R is Relation-like S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of A,A

s is Relation-like S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of A,A

s ** R is Relation-like Function-like Function-yielding Relation-yielding set

dom s is Element of bool S

bool S is set

dom R is Element of bool S

proj1 (s ** R) is set

S /\ S is set

b is Relation-like S -defined Function-like total set

P is set

b . P is set

A . P is set

[:(A . P),(A . P):] is Relation-like set

bool [:(A . P),(A . P):] is set

R . P is Relation-like Function-like set

s . P is Relation-like Function-like set

P is Relation-like A . P -defined A . P -valued Function-like total V29(A . P,A . P) Element of bool [:(A . P),(A . P):]

P is Relation-like A . P -defined A . P -valued Function-like total V29(A . P,A . P) Element of bool [:(A . P),(A . P):]

P * P is Relation-like A . P -defined A . P -valued Function-like total V29(A . P,A . P) Element of bool [:(A . P),(A . P):]

S is non empty non void feasible ManySortedSign

the carrier' of S is non empty set

A is MSAlgebra over S

R is Element of the carrier' of S

Args (R,A) is Element of proj2 K225( the carrier of S, the Sorts of A)

the carrier of S is non empty set

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

K225( the carrier of S, the Sorts of A) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

proj2 K225( the carrier of S, the Sorts of A) is non empty set

s is set

the_arity_of R is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

(the_arity_of R) * the Sorts of A is Relation-like NAT -defined dom (the_arity_of R) -defined Function-like total set

dom (the_arity_of R) is Element of bool NAT

product ((the_arity_of R) * the Sorts of A) is set

dom ((the_arity_of R) * the Sorts of A) is Element of bool NAT

a is Relation-like Function-like set

proj1 a is set

S is non empty non void feasible ManySortedSign

the carrier' of S is non empty set

the carrier of S is non empty set

A is MSAlgebra over S

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

R is Element of the carrier' of S

Args (R,A) is Element of proj2 K225( the carrier of S, the Sorts of A)

K225( the carrier of S, the Sorts of A) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

proj2 K225( the carrier of S, the Sorts of A) is non empty set

the_arity_of R is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

dom (the_arity_of R) is Element of bool NAT

s is Relation-like Function-like set

proj1 s is set

(the_arity_of R) * the Sorts of A is Relation-like NAT -defined dom (the_arity_of R) -defined Function-like total set

product ((the_arity_of R) * the Sorts of A) is set

dom ((the_arity_of R) * the Sorts of A) is Element of bool NAT

a is Relation-like Function-like set

proj1 a is set

a is set

s . a is set

(the_arity_of R) /. a is Element of the carrier of S

the Sorts of A . ((the_arity_of R) /. a) is set

(the_arity_of R) . a is set

((the_arity_of R) * the Sorts of A) . a is set

b is Relation-like Function-like set

proj1 b is set

S is non empty non void feasible ManySortedSign

S is non empty non void feasible ManySortedSign

the carrier' of S is non empty set

the carrier of S is non empty set

A is Element of the carrier' of S

the_arity_of A is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

dom (the_arity_of A) is Element of bool NAT

R is MSAlgebra over S

Args (A,R) is Element of proj2 K225( the carrier of S, the Sorts of R)

the Sorts of R is non empty Relation-like the carrier of S -defined Function-like total set

K225( the carrier of S, the Sorts of R) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of R) is non empty set

(the_arity_of A) * the Sorts of R is Relation-like NAT -defined dom (the_arity_of A) -defined Function-like total set

dom ((the_arity_of A) * the Sorts of R) is Element of bool NAT

product ((the_arity_of A) * the Sorts of R) is set

s is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of A) . s is set

the Sorts of R . ((the_arity_of A) . s) is set

((the_arity_of A) * the Sorts of R) . s is set

(the_arity_of A) /. s is Element of the carrier of S

proj2 ((the_arity_of A) * the Sorts of R) is set

the Sorts of R . ((the_arity_of A) /. s) is set

s is set

((the_arity_of A) * the Sorts of R) . s is set

a is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of A) /. a is Element of the carrier of S

(the_arity_of A) . a is set

the Sorts of R . ((the_arity_of A) /. a) is set

S is non empty non void feasible ManySortedSign

A is MSAlgebra over S

the carrier' of S is non empty set

s is Element of the carrier' of S

Args (s,A) is Element of proj2 K225( the carrier of S, the Sorts of A)

the carrier of S is non empty set

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

K225( the carrier of S, the Sorts of A) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

proj2 K225( the carrier of S, the Sorts of A) is non empty set

Result (s,A) is Element of proj2 the Sorts of A

proj2 the Sorts of A is non empty set

R is non-empty MSAlgebra over S

Result (s,R) is non empty Element of proj2 the Sorts of R

the Sorts of R is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

proj2 the Sorts of R is non empty set

S is non empty non void feasible ManySortedSign

the non-empty (S) MSAlgebra over S is non-empty (S) MSAlgebra over S

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

A is MSAlgebra over S

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

id the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of A, the Sorts of A

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

A is MSAlgebra over S

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

id the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of A, the Sorts of A

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

the carrier' of S is non empty set

A is MSAlgebra over S

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

s is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of A, the Sorts of A

R is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of A, the Sorts of A

( the carrier of S, the Sorts of A,R,s) is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of A, the Sorts of A

b is Element of the carrier' of S

Args (b,A) is Element of proj2 K225( the carrier of S, the Sorts of A)

K225( the carrier of S, the Sorts of A) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

proj2 K225( the carrier of S, the Sorts of A) is non empty set

P is Element of Args (b,A)

R # P is Element of Args (b,A)

s # (R # P) is Element of Args (b,A)

( the carrier of S, the Sorts of A,R,s) # P is Element of Args (b,A)

P is Relation-like Function-like set

proj1 P is set

the_arity_of b is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

dom (the_arity_of b) is Element of bool NAT

(the_arity_of b) * the Sorts of A is Relation-like NAT -defined dom (the_arity_of b) -defined Function-like total set

dom ((the_arity_of b) * the Sorts of A) is Element of bool NAT

product ((the_arity_of b) * the Sorts of A) is set

s is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() set

(the_arity_of b) /. s is Element of the carrier of S

the Sorts of A . ((the_arity_of b) /. s) is set

[:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):] is Relation-like set

bool [:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):] is set

R . ((the_arity_of b) /. s) is Relation-like the Sorts of A . ((the_arity_of b) /. s) -defined the Sorts of A . ((the_arity_of b) /. s) -valued Function-like total V29( the Sorts of A . ((the_arity_of b) /. s), the Sorts of A . ((the_arity_of b) /. s)) Element of bool [:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):]

s . ((the_arity_of b) /. s) is Relation-like the Sorts of A . ((the_arity_of b) /. s) -defined the Sorts of A . ((the_arity_of b) /. s) -valued Function-like total V29( the Sorts of A . ((the_arity_of b) /. s), the Sorts of A . ((the_arity_of b) /. s)) Element of bool [:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):]

( the carrier of S, the Sorts of A,R,s) . ((the_arity_of b) /. s) is Relation-like the Sorts of A . ((the_arity_of b) /. s) -defined the Sorts of A . ((the_arity_of b) /. s) -valued Function-like total V29( the Sorts of A . ((the_arity_of b) /. s), the Sorts of A . ((the_arity_of b) /. s)) Element of bool [:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):]

x is Relation-like the Sorts of A . ((the_arity_of b) /. s) -defined the Sorts of A . ((the_arity_of b) /. s) -valued Function-like total V29( the Sorts of A . ((the_arity_of b) /. s), the Sorts of A . ((the_arity_of b) /. s)) Element of bool [:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):]

y is Relation-like the Sorts of A . ((the_arity_of b) /. s) -defined the Sorts of A . ((the_arity_of b) /. s) -valued Function-like total V29( the Sorts of A . ((the_arity_of b) /. s), the Sorts of A . ((the_arity_of b) /. s)) Element of bool [:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):]

y * x is Relation-like the Sorts of A . ((the_arity_of b) /. s) -defined the Sorts of A . ((the_arity_of b) /. s) -valued Function-like total V29( the Sorts of A . ((the_arity_of b) /. s), the Sorts of A . ((the_arity_of b) /. s)) Element of bool [:( the Sorts of A . ((the_arity_of b) /. s)),( the Sorts of A . ((the_arity_of b) /. s)):]

P . s is set

x . (P . s) is set

P is Relation-like Function-like set

P . s is set

proj1 P is set

y . (P . s) is set

i is Relation-like Function-like set

i . s is set

(the_arity_of b) . s is set

the Sorts of A . ((the_arity_of b) . s) is set

((the_arity_of b) * the Sorts of A) . s is set

(( the carrier of S, the Sorts of A,R,s) . ((the_arity_of b) /. s)) . (P . s) is set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

A is MSAlgebra over S

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

R is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding (S,A)

s is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding (S,A)

( the carrier of S, the Sorts of A,R,s) is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of A, the Sorts of A

the carrier' of S is non empty set

a is Element of the carrier' of S

Args (a,A) is Element of proj2 K225( the carrier of S, the Sorts of A)

K225( the carrier of S, the Sorts of A) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

proj2 K225( the carrier of S, the Sorts of A) is non empty set

the_result_sort_of a is Element of the carrier of S

( the carrier of S, the Sorts of A,R,s) . (the_result_sort_of a) is Relation-like the Sorts of A . (the_result_sort_of a) -defined the Sorts of A . (the_result_sort_of a) -valued Function-like total V29( the Sorts of A . (the_result_sort_of a), the Sorts of A . (the_result_sort_of a)) Element of bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):]

the Sorts of A . (the_result_sort_of a) is set

[:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):] is Relation-like set

bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):] is set

Den (a,A) is Relation-like Args (a,A) -defined Result (a,A) -valued Function-like V29( Args (a,A), Result (a,A)) Element of bool [:(Args (a,A)),(Result (a,A)):]

Result (a,A) is Element of proj2 the Sorts of A

proj2 the Sorts of A is non empty set

[:(Args (a,A)),(Result (a,A)):] is Relation-like set

bool [:(Args (a,A)),(Result (a,A)):] is set

P is Element of Args (a,A)

(Den (a,A)) . P is set

(( the carrier of S, the Sorts of A,R,s) . (the_result_sort_of a)) . ((Den (a,A)) . P) is set

( the carrier of S, the Sorts of A,R,s) # P is Element of Args (a,A)

(Den (a,A)) . (( the carrier of S, the Sorts of A,R,s) # P) is set

R . (the_result_sort_of a) is Relation-like the Sorts of A . (the_result_sort_of a) -defined the Sorts of A . (the_result_sort_of a) -valued Function-like total V29( the Sorts of A . (the_result_sort_of a), the Sorts of A . (the_result_sort_of a)) Element of bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):]

s . (the_result_sort_of a) is Relation-like the Sorts of A . (the_result_sort_of a) -defined the Sorts of A . (the_result_sort_of a) -valued Function-like total V29( the Sorts of A . (the_result_sort_of a), the Sorts of A . (the_result_sort_of a)) Element of bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):]

i is Relation-like the Sorts of A . (the_result_sort_of a) -defined the Sorts of A . (the_result_sort_of a) -valued Function-like total V29( the Sorts of A . (the_result_sort_of a), the Sorts of A . (the_result_sort_of a)) Element of bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):]

dom i is Element of bool ( the Sorts of A . (the_result_sort_of a))

bool ( the Sorts of A . (the_result_sort_of a)) is set

i . ((Den (a,A)) . P) is set

dom (Den (a,A)) is Element of bool (Args (a,A))

bool (Args (a,A)) is set

P is Relation-like the Sorts of A . (the_result_sort_of a) -defined the Sorts of A . (the_result_sort_of a) -valued Function-like total V29( the Sorts of A . (the_result_sort_of a), the Sorts of A . (the_result_sort_of a)) Element of bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):]

P is Relation-like the Sorts of A . (the_result_sort_of a) -defined the Sorts of A . (the_result_sort_of a) -valued Function-like total V29( the Sorts of A . (the_result_sort_of a), the Sorts of A . (the_result_sort_of a)) Element of bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):]

P * P is Relation-like the Sorts of A . (the_result_sort_of a) -defined the Sorts of A . (the_result_sort_of a) -valued Function-like total V29( the Sorts of A . (the_result_sort_of a), the Sorts of A . (the_result_sort_of a)) Element of bool [:( the Sorts of A . (the_result_sort_of a)),( the Sorts of A . (the_result_sort_of a)):]

P . ((Den (a,A)) . P) is set

P . (P . ((Den (a,A)) . P)) is set

R # P is Element of Args (a,A)

(Den (a,A)) . (R # P) is set

(s . (the_result_sort_of a)) . ((Den (a,A)) . (R # P)) is set

s # (R # P) is Element of Args (a,A)

(Den (a,A)) . (s # (R # P)) is set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

A is MSAlgebra over S

R is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding (S,A)

s is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding (S,A)

s ** R is Relation-like Function-like Function-yielding Relation-yielding set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

the carrier' of S is non empty set

A is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

A is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

R is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

S is non empty non void feasible ManySortedSign

the carrier' of S is non empty set

the carrier of S is non empty set

A is Element of the carrier' of S

the_arity_of A is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

R is MSAlgebra over S

Args (A,R) is Element of proj2 K225( the carrier of S, the Sorts of R)

the Sorts of R is non empty Relation-like the carrier of S -defined Function-like total set

K225( the carrier of S, the Sorts of R) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of R) is non empty set

(the_arity_of A) * the Sorts of R is Relation-like NAT -defined dom (the_arity_of A) -defined Function-like total set

dom (the_arity_of A) is Element of bool NAT

dom ((the_arity_of A) * the Sorts of R) is Element of bool NAT

s is Relation-like Function-like set

proj1 s is set

a is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of A) /. a is Element of the carrier of S

the Sorts of R . ((the_arity_of A) /. a) is set

b is Element of the Sorts of R . ((the_arity_of A) /. a)

s +* (a,b) is Relation-like Function-like set

product ((the_arity_of A) * the Sorts of R) is set

P is set

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

((the_arity_of A) * the Sorts of R) . P is set

(the_arity_of A) . P is set

the Sorts of R . ((the_arity_of A) . P) is set

(the_arity_of A) /. P is Element of the carrier of S

((the_arity_of A) * the Sorts of R) . P is set

(s +* (a,b)) . P is set

(s +* (a,b)) . P is set

s . P is set

proj1 (s +* (a,b)) is set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

the carrier' of S is non empty set

A is MSAlgebra over S

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

R is MSAlgebra over S

the Sorts of R is non empty Relation-like the carrier of S -defined Function-like total set

s is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of A, the Sorts of R

a is Element of the carrier' of S

Args (a,A) is Element of proj2 K225( the carrier of S, the Sorts of A)

K225( the carrier of S, the Sorts of A) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

proj2 K225( the carrier of S, the Sorts of A) is non empty set

Args (a,R) is Element of proj2 K225( the carrier of S, the Sorts of R)

K225( the carrier of S, the Sorts of R) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of R) is non empty set

the_arity_of a is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

dom (the_arity_of a) is Element of bool NAT

b is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of a) /. b is Element of the carrier of S

the Sorts of A . ((the_arity_of a) /. b) is set

s . ((the_arity_of a) /. b) is Relation-like the Sorts of A . ((the_arity_of a) /. b) -defined the Sorts of R . ((the_arity_of a) /. b) -valued Function-like V29( the Sorts of A . ((the_arity_of a) /. b), the Sorts of R . ((the_arity_of a) /. b)) Element of bool [:( the Sorts of A . ((the_arity_of a) /. b)),( the Sorts of R . ((the_arity_of a) /. b)):]

the Sorts of R . ((the_arity_of a) /. b) is set

[:( the Sorts of A . ((the_arity_of a) /. b)),( the Sorts of R . ((the_arity_of a) /. b)):] is Relation-like set

bool [:( the Sorts of A . ((the_arity_of a) /. b)),( the Sorts of R . ((the_arity_of a) /. b)):] is set

P is Element of the Sorts of A . ((the_arity_of a) /. b)

(s . ((the_arity_of a) /. b)) . P is set

S is non empty non void feasible ManySortedSign

the carrier' of S is non empty set

the carrier of S is non empty set

A is Element of the carrier' of S

the_arity_of A is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

dom (the_arity_of A) is Element of bool NAT

R is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of A) /. R is Element of the carrier of S

s is MSAlgebra over S

the Sorts of s is non empty Relation-like the carrier of S -defined Function-like total set

a is MSAlgebra over S

the Sorts of a is non empty Relation-like the carrier of S -defined Function-like total set

Args (A,s) is Element of proj2 K225( the carrier of S, the Sorts of s)

K225( the carrier of S, the Sorts of s) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of s) is non empty set

Args (A,a) is Element of proj2 K225( the carrier of S, the Sorts of a)

K225( the carrier of S, the Sorts of a) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of a) is non empty set

the Sorts of s . ((the_arity_of A) /. R) is set

b is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of s, the Sorts of a

b . ((the_arity_of A) /. R) is Relation-like the Sorts of s . ((the_arity_of A) /. R) -defined the Sorts of a . ((the_arity_of A) /. R) -valued Function-like V29( the Sorts of s . ((the_arity_of A) /. R), the Sorts of a . ((the_arity_of A) /. R)) Element of bool [:( the Sorts of s . ((the_arity_of A) /. R)),( the Sorts of a . ((the_arity_of A) /. R)):]

the Sorts of a . ((the_arity_of A) /. R) is set

[:( the Sorts of s . ((the_arity_of A) /. R)),( the Sorts of a . ((the_arity_of A) /. R)):] is Relation-like set

bool [:( the Sorts of s . ((the_arity_of A) /. R)),( the Sorts of a . ((the_arity_of A) /. R)):] is set

P is Element of Args (A,s)

b # P is Element of Args (A,a)

P is Element of Args (A,s)

b # P is Element of Args (A,a)

P is Relation-like Function-like set

proj1 P is set

i is Relation-like Function-like set

s is Relation-like Function-like set

x is Relation-like Function-like set

x . R is set

s +* (R,(x . R)) is Relation-like Function-like set

proj1 i is set

a is Element of the Sorts of s . ((the_arity_of A) /. R)

i +* (R,a) is Relation-like Function-like set

(b . ((the_arity_of A) /. R)) . a is set

P . R is set

y is Relation-like Function-like set

proj1 y is set

b is set

u is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

P . u is set

i . u is set

x . u is set

(the_arity_of A) /. u is Element of the carrier of S

b . ((the_arity_of A) /. u) is Relation-like the Sorts of s . ((the_arity_of A) /. u) -defined the Sorts of a . ((the_arity_of A) /. u) -valued Function-like V29( the Sorts of s . ((the_arity_of A) /. u), the Sorts of a . ((the_arity_of A) /. u)) Element of bool [:( the Sorts of s . ((the_arity_of A) /. u)),( the Sorts of a . ((the_arity_of A) /. u)):]

the Sorts of s . ((the_arity_of A) /. u) is set

the Sorts of a . ((the_arity_of A) /. u) is set

[:( the Sorts of s . ((the_arity_of A) /. u)),( the Sorts of a . ((the_arity_of A) /. u)):] is Relation-like set

bool [:( the Sorts of s . ((the_arity_of A) /. u)),( the Sorts of a . ((the_arity_of A) /. u)):] is set

(b . ((the_arity_of A) /. u)) . (P . u) is set

x . b is set

s . b is set

proj1 s is set

b is set

x . b is set

(s +* (R,(x . R))) . b is set

x . b is set

s . b is set

(s +* (R,(x . R))) . b is set

proj1 x is set

S is non empty non void feasible ManySortedSign

the carrier' of S is non empty set

s is MSAlgebra over S

the Sorts of s is non empty Relation-like the carrier of S -defined Function-like total set

the carrier of S is non empty set

A is Element of the carrier' of S

the_arity_of A is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

R is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of A) /. R is Element of the carrier of S

the Sorts of s . ((the_arity_of A) /. R) is set

Den (A,s) is Relation-like Args (A,s) -defined Result (A,s) -valued Function-like V29( Args (A,s), Result (A,s)) Element of bool [:(Args (A,s)),(Result (A,s)):]

Args (A,s) is Element of proj2 K225( the carrier of S, the Sorts of s)

K225( the carrier of S, the Sorts of s) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of s) is non empty set

Result (A,s) is Element of proj2 the Sorts of s

proj2 the Sorts of s is non empty set

[:(Args (A,s)),(Result (A,s)):] is Relation-like set

bool [:(Args (A,s)),(Result (A,s)):] is set

a is Relation-like Function-like set

b is Relation-like Function-like set

proj1 b is set

b is Relation-like Function-like set

proj1 b is set

P is Relation-like Function-like set

proj1 P is set

P is set

b . P is set

a +* (R,P) is Relation-like Function-like set

(Den (A,s)) . (a +* (R,P)) is set

P . P is set

S is non empty non void feasible ManySortedSign

the carrier' of S is non empty set

the carrier of S is non empty set

A is Element of the carrier' of S

the_arity_of A is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

the_result_sort_of A is Element of the carrier of S

R is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of A) /. R is Element of the carrier of S

s is (S) MSAlgebra over S

Args (A,s) is Element of proj2 K225( the carrier of S, the Sorts of s)

the Sorts of s is non empty Relation-like the carrier of S -defined Function-like total set

K225( the carrier of S, the Sorts of s) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of s) is non empty set

the Sorts of s . ((the_arity_of A) /. R) is set

the Sorts of s . (the_result_sort_of A) is set

[:( the Sorts of s . ((the_arity_of A) /. R)),( the Sorts of s . (the_result_sort_of A)):] is Relation-like set

bool [:( the Sorts of s . ((the_arity_of A) /. R)),( the Sorts of s . (the_result_sort_of A)):] is set

a is Relation-like Function-like set

(S,A,R,s,a) is Relation-like Function-like set

Result (A,s) is Element of proj2 the Sorts of s

proj2 the Sorts of s is non empty set

proj1 (S,A,R,s,a) is set

proj2 (S,A,R,s,a) is set

b is set

P is set

(S,A,R,s,a) . P is set

P is Element of the Sorts of s . ((the_arity_of A) /. R)

a +* (R,P) is Relation-like Function-like set

Den (A,s) is Relation-like Args (A,s) -defined Result (A,s) -valued Function-like V29( Args (A,s), Result (A,s)) Element of bool [:(Args (A,s)),(Result (A,s)):]

[:(Args (A,s)),(Result (A,s)):] is Relation-like set

bool [:(Args (A,s)),(Result (A,s)):] is set

(Den (A,s)) . (a +* (R,P)) is set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

A is Element of the carrier of S

R is Element of the carrier of S

s is (S) MSAlgebra over S

the Sorts of s is non empty Relation-like the carrier of S -defined Function-like total set

the Sorts of s . A is set

the Sorts of s . R is set

[:( the Sorts of s . A),( the Sorts of s . R):] is Relation-like set

bool [:( the Sorts of s . A),( the Sorts of s . R):] is set

a is Relation-like Function-like set

the carrier' of S is non empty set

b is Element of the carrier' of S

the_result_sort_of b is Element of the carrier of S

the_arity_of b is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

dom (the_arity_of b) is Element of bool NAT

Args (b,s) is Element of proj2 K225( the carrier of S, the Sorts of s)

K225( the carrier of S, the Sorts of s) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of s) is non empty set

Result (b,s) is Element of proj2 the Sorts of s

proj2 the Sorts of s is non empty set

the Sorts of s . (the_result_sort_of b) is set

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of b) /. P is Element of the carrier of S

P is Relation-like Function-like set

(S,b,P,s,P) is Relation-like Function-like set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is Element of the carrier of S

R is Element of the carrier of S

[A,R] is V26() set

{A,R} is non empty set

{A} is non empty trivial V42(1) set

{{A,R},{A}} is non empty set

s is MSAlgebra over S

a is Relation-like Function-like set

the carrier' of S is non empty set

b is Element of the carrier' of S

the_result_sort_of b is Element of the carrier of S

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

the_arity_of b is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

dom (the_arity_of b) is Element of bool NAT

(the_arity_of b) /. P is Element of the carrier of S

P is Relation-like Function-like set

Args (b,s) is Element of proj2 K225( the carrier of S, the Sorts of s)

the Sorts of s is non empty Relation-like the carrier of S -defined Function-like total set

K225( the carrier of S, the Sorts of s) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of s) is non empty set

(S,b,P,s,P) is Relation-like Function-like set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is Element of the carrier of S

R is Element of the carrier of S

[A,R] is V26() set

{A,R} is non empty set

{A} is non empty trivial V42(1) set

{{A,R},{A}} is non empty set

s is non-empty (S) MSAlgebra over S

the carrier' of S is non empty set

a is Element of the carrier' of S

the_result_sort_of a is Element of the carrier of S

the_arity_of a is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

dom (the_arity_of a) is Element of bool NAT

Args (a,s) is non empty functional Element of proj2 K225( the carrier of S, the Sorts of s)

the Sorts of s is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

K225( the carrier of S, the Sorts of s) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of s) is non empty set

the Relation-like Function-like Element of Args (a,s) is Relation-like Function-like Element of Args (a,s)

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of a) /. P is Element of the carrier of S

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of a) /. P is Element of the carrier of S

(S,a,P,s, the Relation-like Function-like Element of Args (a,s)) is Relation-like Function-like set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is (S) MSAlgebra over S

the Sorts of A is non empty Relation-like the carrier of S -defined Function-like total set

R is Element of the carrier of S

s is Element of the carrier of S

the Sorts of A . R is set

the Sorts of A . s is set

[:( the Sorts of A . R),( the Sorts of A . s):] is Relation-like set

bool [:( the Sorts of A . R),( the Sorts of A . s):] is set

a is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like RedSequence of (S)

len a is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . 1 is set

a . (len a) is set

b is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

len b is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len b) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

dom b is Element of bool NAT

compose (b,( the Sorts of A . R)) is Relation-like Function-like set

id ( the Sorts of A . R) is Relation-like the Sorts of A . R -defined the Sorts of A . R -valued Function-like one-to-one total V29( the Sorts of A . R, the Sorts of A . R) V30( the Sorts of A . R) V31( the Sorts of A . R, the Sorts of A . R) reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of A . R),( the Sorts of A . R):]

[:( the Sorts of A . R),( the Sorts of A . R):] is Relation-like set

bool [:( the Sorts of A . R),( the Sorts of A . R):] is set

proj2 b is set

1 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

dom a is non empty Element of bool NAT

a . (1 + 1) is set

[(a . 1),(a . (1 + 1))] is V26() set

{(a . 1),(a . (1 + 1))} is non empty set

{(a . 1)} is non empty trivial V42(1) set

{{(a . 1),(a . (1 + 1))},{(a . 1)}} is non empty set

b . 1 is Relation-like Function-like set

Seg (len a) is non empty V35() V42( len a) Element of bool NAT

i is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

len i is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

dom i is Element of bool NAT

P is Element of the carrier of S

P is Element of the carrier of S

P is Relation-like Function-like set

the Sorts of A . P is set

s is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

i . s is set

s + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

i . (s + 1) is set

0 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . s is set

a . (s + 1) is set

[(a . s),(a . (s + 1))] is V26() set

{(a . s),(a . (s + 1))} is non empty set

{(a . s)} is non empty trivial V42(1) set

{{(a . s),(a . (s + 1))},{(a . s)}} is non empty set

b . s is Relation-like Function-like set

x is Element of the carrier of S

y is Element of the carrier of S

a is Relation-like Function-like set

the Sorts of A . y is set

i . 0 is set

s is set

proj1 i is set

i . s is set

Seg (len b) is V35() V42( len b) Element of bool NAT

s is non empty Relation-like non-empty NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

len s is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

x is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

b . x is Relation-like Function-like set

s . x is set

x + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

s . (x + 1) is set

K97((s . x),(s . (x + 1))) is functional set

a . x is set

a . (x + 1) is set

[(a . x),(a . (x + 1))] is V26() set

{(a . x),(a . (x + 1))} is non empty set

{(a . x)} is non empty trivial V42(1) set

{{(a . x),(a . (x + 1))},{(a . x)}} is non empty set

b is Element of the carrier of S

the Sorts of A . b is set

a is Element of the carrier of S

y is Relation-like Function-like set

the Sorts of A . a is set

[:( the Sorts of A . a),( the Sorts of A . b):] is Relation-like set

bool [:( the Sorts of A . a),( the Sorts of A . b):] is set

s . 1 is set

x is Relation-like non-empty NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding FuncSeq-like FuncSequence of s

compose (x,( the Sorts of A . R)) is Relation-like Function-like set

proj1 (compose (x,( the Sorts of A . R))) is set

len s is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

s . (len s) is set

proj2 (compose (x,( the Sorts of A . R))) is set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

R is Element of the carrier of S

s is Element of the carrier of S

A is non-empty (S) MSAlgebra over S

the Sorts of A is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

the Sorts of A . R is non empty set

the Sorts of A . s is non empty set

[:( the Sorts of A . R),( the Sorts of A . s):] is Relation-like set

bool [:( the Sorts of A . R),( the Sorts of A . s):] is set

a is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like RedSequence of (S)

a . 1 is set

len a is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . (len a) is set

0 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

b is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() set

1 + b is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

dom a is non empty Element of bool NAT

Seg (len a) is non empty V35() V42( len a) Element of bool NAT

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

Seg P is V35() V42(P) Element of bool NAT

P is set

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

P + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

P + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . P is set

a . (P + 1) is set

[(a . P),(a . (P + 1))] is V26() set

{(a . P),(a . (P + 1))} is non empty set

{(a . P)} is non empty trivial V42(1) set

{{(a . P),(a . (P + 1))},{(a . P)}} is non empty set

the carrier' of S is non empty set

s is Element of the carrier of S

i is Element of the carrier of S

x is Element of the carrier' of S

the_result_sort_of x is Element of the carrier of S

the_arity_of x is Relation-like NAT -defined the carrier of S -valued Function-like V35() FinSequence-like FinSubsequence-like M13( the carrier of S,K222( the carrier of S))

K222( the carrier of S) is non empty functional FinSequence-membered M12( the carrier of S)

dom (the_arity_of x) is Element of bool NAT

Args (x,A) is non empty functional Element of proj2 K225( the carrier of S, the Sorts of A)

K225( the carrier of S, the Sorts of A) is non empty Relation-like K222( the carrier of S) -defined Function-like total set

proj2 K225( the carrier of S, the Sorts of A) is non empty set

the Relation-like Function-like Element of Args (x,A) is Relation-like Function-like Element of Args (x,A)

a is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of x) /. a is Element of the carrier of S

a is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(the_arity_of x) /. a is Element of the carrier of S

(S,x,a,A, the Relation-like Function-like Element of Args (x,A)) is Relation-like Function-like set

P is Relation-like Function-like set

proj1 P is set

P is set

P . P is set

i is Relation-like Function-like set

y is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

s is Element of the carrier of S

a . y is set

x is Element of the carrier of S

y + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . (y + 1) is set

i is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

P is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

dom P is Element of bool NAT

P . i is Relation-like Function-like set

s is Relation-like Function-like set

x is Element of the carrier of S

a . i is set

y is Element of the carrier of S

i + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . (i + 1) is set

a is Relation-like Function-like set

v is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

b is Element of the carrier of S

a . v is set

u is Element of the carrier of S

v + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . (v + 1) is set

len P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

compose (P,( the Sorts of A . R)) is Relation-like Function-like set

i is non empty Relation-like the Sorts of A . R -defined the Sorts of A . s -valued Function-like total V29( the Sorts of A . R, the Sorts of A . s) Element of bool [:( the Sorts of A . R),( the Sorts of A . s):]

(len P) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

s is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

x is Relation-like Function-like set

P . s is Relation-like Function-like set

y is Element of the carrier of S

a . s is set

a is Element of the carrier of S

s + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . (s + 1) is set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is non-empty (S) MSAlgebra over S

the Sorts of A is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

R is Element of the carrier of S

s is Element of the carrier of S

the Sorts of A . R is non empty set

the Sorts of A . s is non empty set

a is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like RedSequence of (S)

len a is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

a . 1 is set

a . (len a) is set

b is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

len b is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len b) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

dom b is Element of bool NAT

compose (b,( the Sorts of A . R)) is Relation-like Function-like set

[:( the Sorts of A . R),( the Sorts of A . s):] is Relation-like set

bool [:( the Sorts of A . R),( the Sorts of A . s):] is set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

A is non-empty (S) MSAlgebra over S

the Sorts of A is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

R is Element of the carrier of S

the Sorts of A . R is non empty set

id ( the Sorts of A . R) is non empty Relation-like the Sorts of A . R -defined the Sorts of A . R -valued Function-like one-to-one total V29( the Sorts of A . R, the Sorts of A . R) V30( the Sorts of A . R) V31( the Sorts of A . R, the Sorts of A . R) reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of A . R),( the Sorts of A . R):]

[:( the Sorts of A . R),( the Sorts of A . R):] is Relation-like set

bool [:( the Sorts of A . R),( the Sorts of A . R):] is set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

<*R*> is non empty trivial Relation-like NAT -defined the carrier of S -valued Function-like constant V35() V42(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of S

len <*R*> is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

0 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

len {} is empty V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V32() V35() V40() V42( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete Function-yielding Relation-yielding FuncSeq-like irreflexive Element of NAT

dom {} is empty V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V32() V35() V40() V42( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete Function-yielding Relation-yielding FuncSeq-like irreflexive Element of bool NAT

s is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

a is Relation-like Function-like set

{} . s is empty V4() V5() V6() V8() V9() V10() V11() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V32() V35() V40() V42( {} ) FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete Function-yielding Relation-yielding FuncSeq-like irreflexive set

b is Element of the carrier of S

<*R*> . s is set

P is Element of the carrier of S

s + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

<*R*> . (s + 1) is set

<*R*> . 1 is set

compose ({},( the Sorts of A . R)) is Relation-like Function-like set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is non-empty (S) MSAlgebra over S

the Sorts of A is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

R is Element of the carrier of S

s is Element of the carrier of S

the Sorts of A . R is non empty set

the Sorts of A . s is non empty set

a is Relation-like Function-like set

<*R,s*> is non empty Relation-like NAT -defined Function-like V35() V42(2) FinSequence-like FinSubsequence-like set

len <*R,s*> is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

1 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

<*a*> is non empty trivial Relation-like NAT -defined Function-like constant V35() V42(1) FinSequence-like FinSubsequence-like Function-yielding Relation-yielding FuncSeq-like set

len <*a*> is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

[:( the Sorts of A . R),( the Sorts of A . s):] is Relation-like set

bool [:( the Sorts of A . R),( the Sorts of A . s):] is set

<*R,s*> . 2 is set

<*R,s*> . 1 is set

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

dom <*a*> is non empty trivial V42(1) Element of bool NAT

P is Relation-like Function-like set

<*a*> . P is Relation-like Function-like set

P is Element of the carrier of S

<*R,s*> . P is set

i is Element of the carrier of S

P + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

<*R,s*> . (P + 1) is set

b is non empty Relation-like the Sorts of A . R -defined the Sorts of A . s -valued Function-like total V29( the Sorts of A . R, the Sorts of A . s) Element of bool [:( the Sorts of A . R),( the Sorts of A . s):]

dom b is non empty Element of bool ( the Sorts of A . R)

bool ( the Sorts of A . R) is set

compose (<*a*>,( the Sorts of A . R)) is Relation-like Function-like set

[R,s] is V26() set

{R,s} is non empty set

{R} is non empty trivial V42(1) set

{{R,s},{R}} is non empty set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is non-empty (S) MSAlgebra over S

the Sorts of A is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

R is Element of the carrier of S

s is Element of the carrier of S

a is Element of the carrier of S

the Sorts of A . R is non empty set

the Sorts of A . s is non empty set

the Sorts of A . a is non empty set

b is non empty Relation-like the Sorts of A . R -defined the Sorts of A . s -valued Function-like total V29( the Sorts of A . R, the Sorts of A . s) (S,A,R,s)

P is non empty Relation-like the Sorts of A . s -defined the Sorts of A . a -valued Function-like total V29( the Sorts of A . s, the Sorts of A . a) (S,A,s,a)

P * b is non empty Relation-like the Sorts of A . R -defined the Sorts of A . a -valued Function-like total V29( the Sorts of A . R, the Sorts of A . a) Element of bool [:( the Sorts of A . R),( the Sorts of A . a):]

[:( the Sorts of A . R),( the Sorts of A . a):] is Relation-like set

bool [:( the Sorts of A . R),( the Sorts of A . a):] is set

P is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

compose (P,( the Sorts of A . R)) is Relation-like Function-like set

P is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like RedSequence of (S)

len P is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

len P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len P) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

P . 1 is set

P . (len P) is set

dom P is Element of bool NAT

s is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

compose (s,( the Sorts of A . s)) is Relation-like Function-like set

i is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like RedSequence of (S)

len i is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

len s is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len s) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

i . 1 is set

i . (len i) is set

dom s is Element of bool NAT

P $^ i is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

x is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like RedSequence of (S)

len x is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

x . 1 is set

x . (len x) is set

P ^ s is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

y is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

compose (y,( the Sorts of A . R)) is Relation-like Function-like set

len y is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len y) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

dom y is Element of bool NAT

proj2 b is non empty set

(len P) + (len s) is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

a is set

<*a*> is non empty trivial Relation-like NAT -defined Function-like constant V35() V42(1) FinSequence-like FinSubsequence-like set

b is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

<*a*> ^ b is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

len b is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len b) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

u is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

v is set

<*v*> is non empty trivial Relation-like NAT -defined Function-like constant V35() V42(1) FinSequence-like FinSubsequence-like set

u ^ <*v*> is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

u ^ i is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

len <*v*> is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

len u is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len u) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

(len P) + (len i) is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

P ^ b is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

0 + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

Seg (len u) is V35() V42( len u) Element of bool NAT

dom u is Element of bool NAT

u . 1 is set

{} ^ i is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set

dom i is non empty Element of bool NAT

h is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

y . h is Relation-like Function-like set

x . h is set

h + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

x . (h + 1) is set

t is Relation-like Function-like set

s1 is Element of the carrier of S

s2 is Element of the carrier of S

dom P is non empty Element of bool NAT

P . (h + 1) is set

P . h is set

P . h is Relation-like Function-like set

k is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() set

((len P) + 1) + k is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

k + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

(k + 1) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

(len P) + ((k + 1) + 1) is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

1 + k is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

(len P) + (1 + k) is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

i . (k + 1) is set

i . ((k + 1) + 1) is set

s . (k + 1) is Relation-like Function-like set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is non-empty (S) MSAlgebra over S

the Sorts of A is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

R is Element of the carrier of S

s is Element of the carrier of S

the Sorts of A . R is non empty set

the Sorts of A . s is non empty set

a is Element of the carrier of S

the Sorts of A . a is non empty set

b is non empty Relation-like the Sorts of A . R -defined the Sorts of A . s -valued Function-like total V29( the Sorts of A . R, the Sorts of A . s) (S,A,R,s)

P is Relation-like Function-like set

b * P is Relation-like the Sorts of A . R -defined Function-like set

S is non empty non void feasible ManySortedSign

the carrier of S is non empty set

(S) is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]

[: the carrier of S, the carrier of S:] is Relation-like set

bool [: the carrier of S, the carrier of S:] is set

A is non-empty (S) MSAlgebra over S

the Sorts of A is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set

s is Element of the carrier of S

a is Element of the carrier of S

R is Element of the carrier of S

the Sorts of A . s is non empty set

the Sorts of A . a is non empty set

the Sorts of A . R is non empty set

b is Relation-like Function-like set

P is non empty Relation-like the Sorts of A . s -defined the Sorts of A . a -valued Function-like total V29( the Sorts of A . s, the Sorts of A . a) (S,A,s,a)

b * P is Relation-like the Sorts of A . a -valued Function-like set

F

the carrier of F

F

the Sorts of F

(F

[: the carrier of F

bool [: the carrier of F

R is Element of the carrier of F

s is Element of the carrier of F

the Sorts of F

the Sorts of F

a is non empty Relation-like the Sorts of F

P is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

compose (P,( the Sorts of F

b is non empty Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like RedSequence of (F

len b is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

len P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

(len P) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

b . 1 is set

b . (len b) is set

dom P is Element of bool NAT

P is V4() V5() V6() V10() V11() ext-real non negative V32() V35() V40() Element of NAT

Seg P is V35() V42(P) Element of bool NAT

P | (Seg P) is Relation-like NAT -defined Seg P -defined NAT -defined Function-like FinSubsequence-like Function-yielding Relation-yielding set

P + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

b . (P + 1) is set

Seg (P + 1) is non empty V35() V42(P + 1) Element of bool NAT

P | (Seg (P + 1)) is Relation-like NAT -defined Seg (P + 1) -defined NAT -defined Function-like FinSubsequence-like Function-yielding Relation-yielding set

(P + 1) + 1 is non empty V4() V5() V6() V10() V11() ext-real positive non negative V32() V35() V40() Element of NAT

b . ((P + 1) + 1) is set

dom b is non empty Element of bool NAT

[(b . (P + 1)),(b . ((P + 1) + 1))] is V26() set

{(b . (P + 1)),(b . ((P + 1) + 1))} is non empty set

{(b . (P + 1))} is non empty trivial V42(1) set

{{(b . (P + 1)),(b . ((P + 1) + 1))},{(b . (P + 1))}} is non empty set

P . (P + 1) is Relation-like Function-like set

P is Element of the carrier of F

i is Element of the carrier of F

s is Relation-like Function-like set

the Sorts of F

the Sorts of F

x is non empty Relation-like the Sorts of F

P | (Seg 1) is Relation-like NAT -defined Seg 1 -defined NAT -defined Function-like FinSubsequence-like Function-yielding Relation-yielding set

id ( the Sorts of F

[:( the Sorts of F

bool [:( the Sorts of F

y is non empty Relation-like the Sorts of F

y * (id ( the Sorts of F

[:( the Sorts of F

bool [:( the Sorts of F

a is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like Function-yielding Relation-yielding set

compose (a,( the Sorts of F

dom y is non empty Element of bool ( the