:: OSALG_4 semantic presentation

REAL is set
NAT is non empty V4() V5() V6() V47() countable denumerable Element of bool REAL
bool REAL is non empty set
COMPLEX is set
NAT is non empty V4() V5() V6() V47() countable denumerable set
bool NAT is non empty set
bool NAT is non empty set
{} is set
the empty V4() V5() V6() V8() V9() V10() V11() V12() ext-real Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V33() reflexive irreflexive symmetric antisymmetric asymmetric connected strongly_connected transitive V47() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding Relation-yielding Cardinal-yielding countable set is empty V4() V5() V6() V8() V9() V10() V11() V12() ext-real Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional V33() reflexive irreflexive symmetric antisymmetric asymmetric connected strongly_connected transitive V47() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding Relation-yielding Cardinal-yielding countable set
1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive V33() Element of NAT
{{},1} is set
2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive V33() Element of NAT
3 is non empty V4() V5() V6() V10() V11() V12() ext-real positive V33() Element of NAT
0 is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
the Relation-like set is Relation-like set
the carrier of S --> the Relation-like set is non empty Relation-like the carrier of S -defined { the Relation-like set } -valued Function-like constant total V30( the carrier of S,{ the Relation-like set }) Element of bool [: the carrier of S,{ the Relation-like set }:]
{ the Relation-like set } is set
[: the carrier of S,{ the Relation-like set }:] is Relation-like set
bool [: the carrier of S,{ the Relation-like set }:] is non empty set
R is non empty Relation-like the carrier of S -defined Function-like total set
mc is Element of the carrier of S
qa is Element of the carrier of S
R . mc is set
R . qa is set
mc is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
dom mc is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
qa is set
mc . qa is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total set
R is Relation-like set
the carrier of S --> R is non empty Relation-like the carrier of S -defined {R} -valued Function-like constant total V30( the carrier of S,{R}) Element of bool [: the carrier of S,{R}:]
{R} is set
[: the carrier of S,{R}:] is Relation-like set
bool [: the carrier of S,{R}:] is non empty set
qa is non empty Relation-like the carrier of S -defined Function-like total set
S1 is set
qa . S1 is set
U1 . S1 is set
U2 . S1 is set
[:(U1 . S1),(U2 . S1):] is Relation-like set
bool [:(U1 . S1),(U2 . S1):] is non empty set
S1O is Element of the carrier of S
sqa is Element of the carrier of S
U1 . S1O is set
U2 . S1O is set
qa . S1O is set
qa . sqa is set
s1 is set
s2 is set
[s1,s2] is set
{s1,s2} is set
{s1} is set
{{s1,s2},{s1}} is set
S1 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of U1,U2
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of U1,U2
mc is Element of the carrier of S
qa is Element of the carrier of S
F . mc is set
F . qa is set
F . mc is Relation-like U1 . mc -defined U2 . mc -valued Element of bool [:(U1 . mc),(U2 . mc):]
U1 . mc is set
U2 . mc is set
[:(U1 . mc),(U2 . mc):] is Relation-like set
bool [:(U1 . mc),(U2 . mc):] is non empty set
F . qa is Relation-like U1 . qa -defined U2 . qa -valued Element of bool [:(U1 . qa),(U2 . qa):]
U1 . qa is set
U2 . qa is set
[:(U1 . qa),(U2 . qa):] is Relation-like set
bool [:(U1 . qa),(U2 . qa):] is non empty set
qh is set
S1 is set
[qh,S1] is set
{qh,S1} is set
{qh} is set
{{qh,S1},{qh}} is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of U1,U2
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
U1 is order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
the non empty Relation-like the carrier of S -defined Function-like total Relation-yielding order-sorted (S,U2,U2) ManySortedRelation of U2,U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding order-sorted (S,U2,U2) ManySortedRelation of U2,U2
R is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of the Sorts of U1, the Sorts of U1
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
U1 is order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is Relation-like Function-like set
dom U2 is set
F is non empty Relation-like the carrier of S -defined Function-like total set
R is set
F . R is set
the Sorts of U1 . R is set
[:( the Sorts of U1 . R),( the Sorts of U1 . R):] is Relation-like set
bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):] is non empty set
id ( the Sorts of U1 . R) is Relation-like the Sorts of U1 . R -defined the Sorts of U1 . R -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):]
R is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of the Sorts of U1, the Sorts of U1
mc is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of the Sorts of U1, the Sorts of U1
S1 is Element of the carrier of S
S1O is Element of the carrier of S
the Sorts of U1 . S1 is set
mc . S1 is Relation-like the Sorts of U1 . S1 -defined the Sorts of U1 . S1 -valued Element of bool [:( the Sorts of U1 . S1),( the Sorts of U1 . S1):]
[:( the Sorts of U1 . S1),( the Sorts of U1 . S1):] is Relation-like set
bool [:( the Sorts of U1 . S1),( the Sorts of U1 . S1):] is non empty set
mc . S1O is Relation-like the Sorts of U1 . S1O -defined the Sorts of U1 . S1O -valued Element of bool [:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):]
the Sorts of U1 . S1O is set
[:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):] is Relation-like set
bool [:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):] is non empty set
s2 is set
a1 is set
[s2,a1] is set
{s2,a1} is set
{s2} is set
{{s2,a1},{s2}} is set
qh is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
qh . S1 is set
id (qh . S1) is Relation-like qh . S1 -defined qh . S1 -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:(qh . S1),(qh . S1):]
[:(qh . S1),(qh . S1):] is Relation-like set
bool [:(qh . S1),(qh . S1):] is non empty set
qh . S1O is set
id (qh . S1O) is Relation-like qh . S1O -defined qh . S1O -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:(qh . S1O),(qh . S1O):]
[:(qh . S1O),(qh . S1O):] is Relation-like set
bool [:(qh . S1O),(qh . S1O):] is non empty set
sqa is Element of the carrier of S
qh . sqa is set
s1 is Element of the carrier of S
qh . s1 is set
qh is set
the Sorts of U1 . qh is set
[:( the Sorts of U1 . qh),( the Sorts of U1 . qh):] is Relation-like set
bool [:( the Sorts of U1 . qh),( the Sorts of U1 . qh):] is non empty set
mc . qh is set
S1 is Relation-like the Sorts of U1 . qh -defined the Sorts of U1 . qh -valued Element of bool [:( the Sorts of U1 . qh),( the Sorts of U1 . qh):]
id ( the Sorts of U1 . qh) is Relation-like the Sorts of U1 . qh -defined the Sorts of U1 . qh -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of U1 . qh),( the Sorts of U1 . qh):]
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is Relation-like Function-like set
dom U2 is set
F is non empty Relation-like the carrier of S -defined Function-like total set
R is set
F . R is set
the Sorts of U1 . R is set
[:( the Sorts of U1 . R),( the Sorts of U1 . R):] is Relation-like set
bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):] is non empty set
id ( the Sorts of U1 . R) is Relation-like the Sorts of U1 . R -defined the Sorts of U1 . R -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):]
R is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of the Sorts of U1, the Sorts of U1
mc is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding ManySortedRelation of the Sorts of U1, the Sorts of U1
qa is set
the Sorts of U1 . qa is set
[:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is Relation-like set
bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is non empty set
mc . qa is set
qh is Relation-like the Sorts of U1 . qa -defined the Sorts of U1 . qa -valued Element of bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):]
id ( the Sorts of U1 . qa) is Relation-like the Sorts of U1 . qa -defined the Sorts of U1 . qa -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):]
qa is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
S1O is Element of the carrier of S
sqa is Element of the carrier of S
the Sorts of U1 . S1O is non empty set
qa . S1O is Relation-like the Sorts of U1 . S1O -defined the Sorts of U1 . S1O -valued Element of bool [:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):]
[:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):] is non empty Relation-like set
bool [:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):] is non empty set
qa . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
the Sorts of U1 . sqa is non empty set
[:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty Relation-like set
bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty set
a1 is set
x is set
[a1,x] is set
{a1,x} is set
{a1} is set
{{a1,x},{a1}} is set
qa . S1O is Relation-like the Sorts of U1 . S1O -defined the Sorts of U1 . S1O -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):]
S1 is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
S1 . S1O is set
id (S1 . S1O) is Relation-like S1 . S1O -defined S1 . S1O -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:(S1 . S1O),(S1 . S1O):]
[:(S1 . S1O),(S1 . S1O):] is Relation-like set
bool [:(S1 . S1O),(S1 . S1O):] is non empty set
qa . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
S1 . sqa is set
id (S1 . sqa) is Relation-like S1 . sqa -defined S1 . sqa -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:(S1 . sqa),(S1 . sqa):]
[:(S1 . sqa),(S1 . sqa):] is Relation-like set
bool [:(S1 . sqa),(S1 . sqa):] is non empty set
s1 is Element of the carrier of S
S1 . s1 is set
s2 is Element of the carrier of S
S1 . s2 is set
S1 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
the carrier' of S is non empty set
S1O is Element of the carrier' of S
Args (S1O,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
the_arity_of S1O is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
Result (S1O,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (S1O,U1) is Relation-like Args (S1O,U1) -defined Result (S1O,U1) -valued Function-like V30( Args (S1O,U1), Result (S1O,U1)) Element of bool [:(Args (S1O,U1)),(Result (S1O,U1)):]
[:(Args (S1O,U1)),(Result (S1O,U1)):] is non empty Relation-like set
bool [:(Args (S1O,U1)),(Result (S1O,U1)):] is non empty set
the_result_sort_of S1O is Element of the carrier of S
S1 . (the_result_sort_of S1O) is Relation-like the Sorts of U1 . (the_result_sort_of S1O) -defined the Sorts of U1 . (the_result_sort_of S1O) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of S1O)),( the Sorts of U1 . (the_result_sort_of S1O)):]
the Sorts of U1 . (the_result_sort_of S1O) is non empty set
[:( the Sorts of U1 . (the_result_sort_of S1O)),( the Sorts of U1 . (the_result_sort_of S1O)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of S1O)),( the Sorts of U1 . (the_result_sort_of S1O)):] is non empty set
sqa is Relation-like Function-like Element of Args (S1O,U1)
dom sqa is set
s1 is Relation-like Function-like Element of Args (S1O,U1)
(Den (S1O,U1)) . sqa is Element of Result (S1O,U1)
(Den (S1O,U1)) . s1 is Element of Result (S1O,U1)
[((Den (S1O,U1)) . sqa),((Den (S1O,U1)) . s1)] is set
{((Den (S1O,U1)) . sqa),((Den (S1O,U1)) . s1)} is set
{((Den (S1O,U1)) . sqa)} is set
{{((Den (S1O,U1)) . sqa),((Den (S1O,U1)) . s1)},{((Den (S1O,U1)) . sqa)}} is set
dom (the_arity_of S1O) is countable Element of bool NAT
a1 is set
sqa . a1 is set
s1 . a1 is set
x is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of S1O) . x is set
rng (the_arity_of S1O) is Element of bool the carrier of S
bool the carrier of S is non empty set
S1 . ((the_arity_of S1O) . x) is set
the Sorts of U1 . ((the_arity_of S1O) . x) is set
id ( the Sorts of U1 . ((the_arity_of S1O) . x)) is Relation-like the Sorts of U1 . ((the_arity_of S1O) . x) -defined the Sorts of U1 . ((the_arity_of S1O) . x) -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of U1 . ((the_arity_of S1O) . x)),( the Sorts of U1 . ((the_arity_of S1O) . x)):]
[:( the Sorts of U1 . ((the_arity_of S1O) . x)),( the Sorts of U1 . ((the_arity_of S1O) . x)):] is Relation-like set
bool [:( the Sorts of U1 . ((the_arity_of S1O) . x)),( the Sorts of U1 . ((the_arity_of S1O) . x)):] is non empty set
(the_arity_of S1O) /. x is Element of the carrier of S
sqa . x is set
s1 . x is set
[(sqa . x),(s1 . x)] is set
{(sqa . x),(s1 . x)} is set
{(sqa . x)} is set
{{(sqa . x),(s1 . x)},{(sqa . x)}} is set
id ( the Sorts of U1 . (the_result_sort_of S1O)) is non empty Relation-like the Sorts of U1 . (the_result_sort_of S1O) -defined the Sorts of U1 . (the_result_sort_of S1O) -valued Function-like one-to-one total reflexive symmetric antisymmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of S1O)),( the Sorts of U1 . (the_result_sort_of S1O)):]
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
dom the ResultSort of S is Element of bool the carrier' of S
bool the carrier' of S is non empty set
the ResultSort of S * the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
dom ( the ResultSort of S * the Sorts of U1) is non empty Element of bool the carrier' of S
( the ResultSort of S * the Sorts of U1) . S1O is non empty set
the ResultSort of S . S1O is Element of the carrier of S
the Sorts of U1 . ( the ResultSort of S . S1O) is non empty set
dom s1 is set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
the InternalRel of 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:]
{ [b₁,b₂] where b₁, b₂ is Element of the carrier of S : ( b₁ in the carrier of S & b₂ in the carrier of S & S₁[b₁,b₂] ) } is set
U2 is set
F is Element of the carrier of S
R is Element of the carrier of S
[F,R] is set
{F,R} is set
{F} is set
{{F,R},{F}} is set
mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len mc is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
mc . 1 is set
mc . (len mc) is set
F is set
R is set
[F,R] is set
{F,R} is set
{F} is set
{{F,R},{F}} is set
mc is Element of the carrier of S
qa is Element of the carrier of S
[mc,qa] is set
{mc,qa} is set
{mc} is set
{{mc,qa},{mc}} is set
qh is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len qh is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qh . 1 is set
qh . (len qh) is set
mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len mc is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
mc . 1 is set
mc . (len mc) is set
F is set
R is set
[F,R] is set
{F,R} is set
{F} is set
{{F,R},{F}} is set
U2 is Relation-like the carrier of S -defined the carrier of S -valued Element of bool [: the carrier of S, the carrier of S:]
mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len mc is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
mc . 1 is set
mc . (len mc) is set
Rev mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
qa is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len qa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qa . 1 is set
qa . (len qa) is set
qh is V4() V5() V6() V10() V11() V12() ext-real V33() set
qa . qh is set
qh - 1 is V11() V12() ext-real V33() set
qa . (qh - 1) is set
[(qa . qh),(qa . (qh - 1))] is set
{(qa . qh),(qa . (qh - 1))} is set
{(qa . qh)} is set
{{(qa . qh),(qa . (qh - 1))},{(qa . qh)}} is set
[(qa . (qh - 1)),(qa . qh)] is set
{(qa . (qh - 1)),(qa . qh)} is set
{(qa . (qh - 1))} is set
{{(qa . (qh - 1)),(qa . qh)},{(qa . (qh - 1))}} is set
dom mc is countable Element of bool NAT
(len mc) - qh is V11() V12() ext-real V33() set
((len mc) - qh) + 2 is V11() V12() ext-real V33() set
2 + 0 is V11() V12() ext-real V33() set
2 - 1 is V11() V12() ext-real V33() set
(len qa) - 0 is V11() V12() ext-real V33() set
S1O is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
(len mc) - (qh - 1) is V11() V12() ext-real V33() set
((len mc) - (qh - 1)) + 1 is V11() V12() ext-real V33() set
mc . (((len mc) - (qh - 1)) + 1) is set
mc . (((len mc) - qh) + 2) is set
(len mc) - 2 is V11() V12() ext-real V33() set
((len mc) - 2) + 2 is V11() V12() ext-real V33() set
sqa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
sqa - 1 is V11() V12() ext-real V33() set
mc . (sqa - 1) is set
((len mc) - qh) + (2 - 1) is V11() V12() ext-real V33() set
mc . (((len mc) - qh) + (2 - 1)) is set
[R,F] is set
{R,F} is set
{R} is set
{{R,F},{R}} is set
qa is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len qa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qa . 1 is set
qa . (len qa) is set
F is set
<*F,F*> is non empty Relation-like NAT -defined Function-like V47() V54(2) FinSequence-like FinSubsequence-like countable set
rng <*F,F*> is non empty set
{F,F} is set
{F} is set
mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len mc is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
mc . 1 is set
mc . (len mc) is set
len <*F,F*> is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qa is V4() V5() V6() V10() V11() V12() ext-real V33() set
mc . qa is set
qa - 1 is V11() V12() ext-real V33() set
mc . (qa - 1) is set
[(mc . qa),(mc . (qa - 1))] is set
{(mc . qa),(mc . (qa - 1))} is set
{(mc . qa)} is set
{{(mc . qa),(mc . (qa - 1))},{(mc . qa)}} is set
[(mc . (qa - 1)),(mc . qa)] is set
{(mc . (qa - 1)),(mc . qa)} is set
{(mc . (qa - 1))} is set
{{(mc . (qa - 1)),(mc . qa)},{(mc . (qa - 1))}} is set
<*F,F*> . 1 is set
<*F,F*> . 2 is set
[F,F] is set
{F,F} is set
{F} is set
{{F,F},{F}} is set
R is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len R is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
R . 1 is set
R . (len R) is set
dom U2 is Element of bool the carrier of S
bool the carrier of S is non empty set
field U2 is set
F is set
R is set
mc is set
[F,R] is set
{F,R} is set
{F} is set
{{F,R},{F}} is set
[R,mc] is set
{R,mc} is set
{R} is set
{{R,mc},{R}} is set
qa is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len qa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qa . 1 is set
qa . (len qa) is set
qh is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len qh is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qh . 1 is set
qh . (len qh) is set
qa is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len qa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qa . 1 is set
qa . (len qa) is set
qh is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len qh is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qh . 1 is set
qh . (len qh) is set
qa ^ qh is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
S1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len S1 is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
S1 . 1 is set
S1 . (len S1) is set
(len qa) + (len qh) is V11() V12() ext-real V33() set
1 + 1 is V11() V12() ext-real V33() set
dom qa is countable Element of bool NAT
dom qh is countable Element of bool NAT
S1O is V4() V5() V6() V10() V11() V12() ext-real V33() set
S1 . S1O is set
S1O - 1 is V11() V12() ext-real V33() set
S1 . (S1O - 1) is set
[(S1 . S1O),(S1 . (S1O - 1))] is set
{(S1 . S1O),(S1 . (S1O - 1))} is set
{(S1 . S1O)} is set
{{(S1 . S1O),(S1 . (S1O - 1))},{(S1 . S1O)}} is set
[(S1 . (S1O - 1)),(S1 . S1O)] is set
{(S1 . (S1O - 1)),(S1 . S1O)} is set
{(S1 . (S1O - 1))} is set
{{(S1 . (S1O - 1)),(S1 . S1O)},{(S1 . (S1O - 1))}} is set
2 - 1 is V11() V12() ext-real V33() set
(len qa) + 1 is V11() V12() ext-real V33() set
(len S1) - 0 is V11() V12() ext-real V33() set
(len qa) - 0 is V11() V12() ext-real V33() set
sqa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
qa . (S1O - 1) is set
qa . S1O is set
S1O - (len qa) is V11() V12() ext-real V33() set
((len qa) + 1) - 1 is V11() V12() ext-real V33() set
sqa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
S1 . sqa is set
sqa - (len qa) is V11() V12() ext-real V33() set
qh . (sqa - (len qa)) is set
s1 is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
s1 - 1 is V11() V12() ext-real V33() set
qh . (s1 - 1) is set
qh . s1 is set
((len qa) + 1) - (len qa) is V11() V12() ext-real V33() set
[F,mc] is set
{F,mc} is set
{{F,mc},{F}} is set
S1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len S1 is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
S1 . 1 is set
S1 . (len S1) is set
F is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
R is set
mc is set
[R,mc] is set
{R,mc} is set
{R} is set
{{R,mc},{R}} is set
qa is set
qh is set
S1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len S1 is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
S1 . 1 is set
S1 . (len S1) is set
[qa,qh] is set
{qa,qh} is set
{qa} is set
{{qa,qh},{qa}} is set
U1 is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
U2 is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
F is set
R is set
[F,R] is set
{F,R} is set
{F} is set
{{F,R},{F}} is set
mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len mc is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
mc . 1 is set
mc . (len mc) is set
mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len mc is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
mc . 1 is set
mc . (len mc) is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
U1 is Element of the carrier of S
U2 is Element of the carrier of S
[U1,U2] is set
{U1,U2} is set
{U1} is set
{{U1,U2},{U1}} is set
<*U1,U2*> is non empty Relation-like NAT -defined the carrier of S -valued Function-like V47() V54(2) FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len <*U1,U2*> is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
<*U1,U2*> . 1 is set
the InternalRel of 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:]
R is V4() V5() V6() V10() V11() V12() ext-real V33() set
<*U1,U2*> . R is set
R - 1 is V11() V12() ext-real V33() set
<*U1,U2*> . (R - 1) is set
[(<*U1,U2*> . R),(<*U1,U2*> . (R - 1))] is set
{(<*U1,U2*> . R),(<*U1,U2*> . (R - 1))} is set
{(<*U1,U2*> . R)} is set
{{(<*U1,U2*> . R),(<*U1,U2*> . (R - 1))},{(<*U1,U2*> . R)}} is set
[(<*U1,U2*> . (R - 1)),(<*U1,U2*> . R)] is set
{(<*U1,U2*> . (R - 1)),(<*U1,U2*> . R)} is set
{(<*U1,U2*> . (R - 1))} is set
{{(<*U1,U2*> . (R - 1)),(<*U1,U2*> . R)},{(<*U1,U2*> . (R - 1))}} is set
<*U1,U2*> . (len <*U1,U2*>) is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
field (S) is set
R is Element of the carrier of S
[R,R] is set
{R,R} is set
{R} is set
{{R,R},{R}} is set
field (S) is set
R is Element of the carrier of S
mc is Element of the carrier of S
[R,mc] is set
{R,mc} is set
{R} is set
{{R,mc},{R}} is set
[mc,R] is set
{mc,R} is set
{mc} is set
{{mc,R},{mc}} is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
U1 is Element of the carrier of S
U2 is Element of the carrier of S
F is Element of the carrier of S
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
field (S) is set
[U1,U2] is set
{U1,U2} is set
{U1} is set
{{U1,U2},{U1}} is set
[U2,F] is set
{U2,F} is set
{U2} is set
{{U2,F},{U2}} is set
[U1,F] is set
{U1,F} is set
{{U1,F},{U1}} is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
bool the carrier of S is non empty set
bool (bool the carrier of S) is non empty set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
U1 is Element of (S)
U2 is set
Class ((S),U2) is Element of bool the carrier of S
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
U1 is Element of the carrier of S
Class ((S),U1) is Element of bool the carrier of S
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
U1 is Element of the carrier of S
U2 is Element of the carrier of S
(S,U1) is non empty Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),U1) is Element of bool the carrier of S
(S,U2) is non empty Element of (S)
Class ((S),U2) is Element of bool the carrier of S
[U1,U2] is set
{U1,U2} is set
{U1} is set
{{U1,U2},{U1}} is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Element of (S)
{ (U1 . b₁) where b₁ is Element of the carrier of S : b₁ in U2 } is set
union { (U1 . b₁) where b₁ is Element of the carrier of S : b₁ in U2 } is set
S is non empty reflexive transitive antisymmetric RelStr
the carrier of S is non empty set
U1 is non empty Relation-like the carrier of S -defined Function-like total set
U2 is Element of the carrier of S
U1 . U2 is set
(S,U2) is non empty Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),U2) is Element of bool the carrier of S
(S,U1,(S,U2)) is set
{ (U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,U2) } is set
union { (U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,U2) } is set
F is set
S is non empty reflexive transitive antisymmetric discrete RelStr
the carrier of S is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
U1 is Element of the carrier of S
U2 is Element of the carrier of S
[U1,U2] is set
{U1,U2} is set
{U1} is set
{{U1,U2},{U1}} is set
the InternalRel of 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:]
F is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable FinSequence of the carrier of S
len F is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
F . 1 is set
F . (len F) is set
R is V4() V5() V6() V10() V11() V12() ext-real V33() set
F . R is set
mc is V4() V5() V6() V10() V11() V12() ext-real V33() set
F . mc is set
1 + 1 is V11() V12() ext-real V33() set
(1 + 1) - 1 is V11() V12() ext-real V33() set
mc - 1 is V11() V12() ext-real V33() set
qa is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
F . qa is set
dom F is countable Element of bool NAT
qh is Element of the carrier of S
[qh,U1] is set
{qh,U1} is set
{qh} is set
{{qh,U1},{qh}} is set
qh is Element of the carrier of S
[U1,qh] is set
{U1,qh} is set
{{U1,qh},{U1}} is set
qh is Element of the carrier of S
[qh,U1] is set
{qh,U1} is set
{qh} is set
{{qh,U1},{qh}} is set
[U1,qh] is set
{U1,qh} is set
{{U1,qh},{U1}} is set
S is non empty reflexive transitive antisymmetric discrete RelStr
the carrier of S is non empty set
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
U1 is non empty Element of (S)
U2 is set
Class ((S),U2) is Element of bool the carrier of S
F is Element of the carrier of S
{F} is set
R is set
[R,U2] is set
{R,U2} is set
{R} is set
{{R,U2},{R}} is set
mc is Element of the carrier of S
S is non empty reflexive transitive antisymmetric discrete RelStr
the carrier of S is non empty set
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
U1 is non empty Element of (S)
U2 is Element of the carrier of S
{U2} is set
F is Element of the carrier of S
R is Element of the carrier of S
the non empty reflexive transitive antisymmetric discrete RelStr is non empty reflexive transitive antisymmetric discrete RelStr
the non empty non void V73() reflexive transitive antisymmetric discrete order-sorted discernable OverloadedRSSign is non empty non void V73() reflexive transitive antisymmetric discrete order-sorted discernable OverloadedRSSign
S is non empty reflexive transitive antisymmetric RelStr
S is non empty reflexive transitive antisymmetric () RelStr
the carrier of S is non empty set
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
U1 is non empty Element of (S)
[:{},{}:] is Relation-like set
bool [:{},{}:] is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is order-sorted MSAlgebra over S
the carrier of S is non empty set
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
the Sorts of U1 is non empty Relation-like the carrier of S -defined Function-like total set
F is non empty directed Element of (S)
(S, the Sorts of U1,F) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in F } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in F } is set
[:(S, the Sorts of U1,F),(S, the Sorts of U1,F):] is Relation-like set
bool [:(S, the Sorts of U1,F),(S, the Sorts of U1,F):] is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
R is set
mc is set
[R,mc] is set
{R,mc} is set
{R} is set
{{R,mc},{R}} is set
qa is Element of the carrier of S
U2 . qa is Relation-like the Sorts of U1 . qa -defined the Sorts of U1 . qa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):]
the Sorts of U1 . qa is set
[:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is Relation-like set
bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is non empty set
qa is Element of the carrier of S
U2 . qa is Relation-like the Sorts of U1 . qa -defined the Sorts of U1 . qa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):]
the Sorts of U1 . qa is set
[:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is Relation-like set
bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is non empty set
R is non empty set
{ [b₁,b₂] where b₁, b₂ is Element of R : S₁[b₁,b₂] } is set
[:R,R:] is non empty Relation-like set
qa is set
qh is Element of R
S1 is Element of R
[qh,S1] is set
{qh,S1} is set
{qh} is set
{{qh,S1},{qh}} is set
S1O is Element of the carrier of S
U2 . S1O is Relation-like the Sorts of U1 . S1O -defined the Sorts of U1 . S1O -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):]
the Sorts of U1 . S1O is set
[:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):] is Relation-like set
bool [:( the Sorts of U1 . S1O),( the Sorts of U1 . S1O):] is non empty set
bool [:R,R:] is non empty set
qh is set
S1 is set
[qh,S1] is set
{qh,S1} is set
{qh} is set
{{qh,S1},{qh}} is set
qa is Relation-like R -defined R -valued Element of bool [:R,R:]
s1 is Element of R
s2 is Element of R
[s1,s2] is set
{s1,s2} is set
{s1} is set
{{s1,s2},{s1}} is set
a1 is Element of the carrier of S
U2 . a1 is Relation-like the Sorts of U1 . a1 -defined the Sorts of U1 . a1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . a1),( the Sorts of U1 . a1):]
the Sorts of U1 . a1 is set
[:( the Sorts of U1 . a1),( the Sorts of U1 . a1):] is Relation-like set
bool [:( the Sorts of U1 . a1),( the Sorts of U1 . a1):] is non empty set
a1 is Element of the carrier of S
U2 . a1 is Relation-like the Sorts of U1 . a1 -defined the Sorts of U1 . a1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . a1),( the Sorts of U1 . a1):]
the Sorts of U1 . a1 is set
[:( the Sorts of U1 . a1),( the Sorts of U1 . a1):] is Relation-like set
bool [:( the Sorts of U1 . a1),( the Sorts of U1 . a1):] is non empty set
field (U2 . a1) is set
[S1,qh] is set
{S1,qh} is set
{S1} is set
{{S1,qh},{S1}} is set
sqa is Element of R
S1O is Element of R
[sqa,S1O] is set
{sqa,S1O} is set
{sqa} is set
{{sqa,S1O},{sqa}} is set
qh is set
S1O is set
sqa is Element of the carrier of S
the Sorts of U1 . sqa is set
U2 . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
[:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is Relation-like set
bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty set
field (U2 . sqa) is set
[qh,qh] is set
{qh,qh} is set
{qh} is set
{{qh,qh},{qh}} is set
S1 is Element of R
[S1,S1] is set
{S1,S1} is set
{S1} is set
{{S1,S1},{S1}} is set
dom qa is Element of bool R
bool R is non empty set
field qa is set
qh is set
S1 is set
S1O is set
[qh,S1] is set
{qh,S1} is set
{qh} is set
{{qh,S1},{qh}} is set
[S1,S1O] is set
{S1,S1O} is set
{S1} is set
{{S1,S1O},{S1}} is set
sqa is Element of R
s1 is Element of R
[sqa,s1] is set
{sqa,s1} is set
{sqa} is set
{{sqa,s1},{sqa}} is set
s2 is Element of R
a1 is Element of R
[s2,a1] is set
{s2,a1} is set
{s2} is set
{{s2,a1},{s2}} is set
x is Element of the carrier of S
U2 . x is Relation-like the Sorts of U1 . x -defined the Sorts of U1 . x -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . x),( the Sorts of U1 . x):]
the Sorts of U1 . x is set
[:( the Sorts of U1 . x),( the Sorts of U1 . x):] is Relation-like set
bool [:( the Sorts of U1 . x),( the Sorts of U1 . x):] is non empty set
x is Element of the carrier of S
U2 . x is Relation-like the Sorts of U1 . x -defined the Sorts of U1 . x -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . x),( the Sorts of U1 . x):]
the Sorts of U1 . x is set
[:( the Sorts of U1 . x),( the Sorts of U1 . x):] is Relation-like set
bool [:( the Sorts of U1 . x),( the Sorts of U1 . x):] is non empty set
x2 is Element of the carrier of S
U2 . x2 is Relation-like the Sorts of U1 . x2 -defined the Sorts of U1 . x2 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . x2),( the Sorts of U1 . x2):]
the Sorts of U1 . x2 is set
[:( the Sorts of U1 . x2),( the Sorts of U1 . x2):] is Relation-like set
bool [:( the Sorts of U1 . x2),( the Sorts of U1 . x2):] is non empty set
x2 is Element of the carrier of S
U2 . x2 is Relation-like the Sorts of U1 . x2 -defined the Sorts of U1 . x2 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . x2),( the Sorts of U1 . x2):]
the Sorts of U1 . x2 is set
[:( the Sorts of U1 . x2),( the Sorts of U1 . x2):] is Relation-like set
bool [:( the Sorts of U1 . x2),( the Sorts of U1 . x2):] is non empty set
s3 is Element of the carrier of S
s4 is Element of the carrier of S
x1 is Element of the carrier of S
U2 . x1 is Relation-like the Sorts of U1 . x1 -defined the Sorts of U1 . x1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . x1),( the Sorts of U1 . x1):]
the Sorts of U1 . x1 is set
[:( the Sorts of U1 . x1),( the Sorts of U1 . x1):] is Relation-like set
bool [:( the Sorts of U1 . x1),( the Sorts of U1 . x1):] is non empty set
field (U2 . x1) is set
[sqa,a1] is set
{sqa,a1} is set
{{sqa,a1},{sqa}} is set
[qh,S1O] is set
{qh,S1O} is set
{{qh,S1O},{qh}} is set
qh is Relation-like (S, the Sorts of U1,F) -defined (S, the Sorts of U1,F) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,F),(S, the Sorts of U1,F):]
S1 is set
S1O is set
[S1,S1O] is set
{S1,S1O} is set
{S1} is set
{{S1,S1O},{S1}} is set
sqa is Element of R
s1 is Element of R
[sqa,s1] is set
{sqa,s1} is set
{sqa} is set
{{sqa,s1},{sqa}} is set
s2 is Element of the carrier of S
U2 . s2 is Relation-like the Sorts of U1 . s2 -defined the Sorts of U1 . s2 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . s2),( the Sorts of U1 . s2):]
the Sorts of U1 . s2 is set
[:( the Sorts of U1 . s2),( the Sorts of U1 . s2):] is Relation-like set
bool [:( the Sorts of U1 . s2),( the Sorts of U1 . s2):] is non empty set
sqa is Element of the carrier of S
U2 . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
the Sorts of U1 . sqa is set
[:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is Relation-like set
bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty set
sqa is Element of the carrier of S
U2 . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
the Sorts of U1 . sqa is set
[:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is Relation-like set
bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty set
s1 is Element of R
s2 is Element of R
[s1,s2] is set
{s1,s2} is set
{s1} is set
{{s1,s2},{s1}} is set
a1 is Element of the carrier of S
U2 . a1 is Relation-like the Sorts of U1 . a1 -defined the Sorts of U1 . a1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . a1),( the Sorts of U1 . a1):]
the Sorts of U1 . a1 is set
[:( the Sorts of U1 . a1),( the Sorts of U1 . a1):] is Relation-like set
bool [:( the Sorts of U1 . a1),( the Sorts of U1 . a1):] is non empty set
S1 is set
S1O is set
[S1,S1O] is set
{S1,S1O} is set
{S1} is set
{{S1,S1O},{S1}} is set
s2 is Element of the carrier of S
sqa is set
s1 is set
[sqa,s1] is set
{sqa,s1} is set
{sqa} is set
{{sqa,s1},{sqa}} is set
U2 . s2 is Relation-like the Sorts of U1 . s2 -defined the Sorts of U1 . s2 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . s2),( the Sorts of U1 . s2):]
the Sorts of U1 . s2 is set
[:( the Sorts of U1 . s2),( the Sorts of U1 . s2):] is Relation-like set
bool [:( the Sorts of U1 . s2),( the Sorts of U1 . s2):] is non empty set
R is Relation-like (S, the Sorts of U1,F) -defined (S, the Sorts of U1,F) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,F),(S, the Sorts of U1,F):]
mc is Relation-like (S, the Sorts of U1,F) -defined (S, the Sorts of U1,F) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,F),(S, the Sorts of U1,F):]
qa is set
qh is set
[qa,qh] is set
{qa,qh} is set
{qa} is set
{{qa,qh},{qa}} is set
S1 is Element of the carrier of S
U2 . S1 is Relation-like the Sorts of U1 . S1 -defined the Sorts of U1 . S1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . S1),( the Sorts of U1 . S1):]
the Sorts of U1 . S1 is set
[:( the Sorts of U1 . S1),( the Sorts of U1 . S1):] is Relation-like set
bool [:( the Sorts of U1 . S1),( the Sorts of U1 . S1):] is non empty set
S1 is Element of the carrier of S
U2 . S1 is Relation-like the Sorts of U1 . S1 -defined the Sorts of U1 . S1 -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . S1),( the Sorts of U1 . S1):]
the Sorts of U1 . S1 is set
[:( the Sorts of U1 . S1),( the Sorts of U1 . S1):] is Relation-like set
bool [:( the Sorts of U1 . S1),( the Sorts of U1 . S1):] is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of U1 is non empty Relation-like the carrier of S -defined Function-like total set
F is Element of the carrier of S
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S, the Sorts of U1,(S,F)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
(S,U1,U2,(S,F)) is Relation-like (S, the Sorts of U1,(S,F)) -defined (S, the Sorts of U1,(S,F)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):]
[:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is non empty set
Class (S,U1,U2,(S,F)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,F))
bool (Class (S,U1,U2,(S,F))) is non empty set
the Sorts of U1 . F is set
qa is Element of bool (Class (S,U1,U2,(S,F)))
qh is set
S1 is set
Class ((S,U1,U2,(S,F)),S1) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
S1 is set
Class ((S,U1,U2,(S,F)),S1) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
bool (S, the Sorts of U1,(S,F)) is non empty set
bool (bool (S, the Sorts of U1,(S,F))) is non empty set
qa is non empty Element of bool (bool (S, the Sorts of U1,(S,F)))
{ b₁ where b₁ is Element of qa : S₁[b₁] } is set
S1 is set
S1O is Element of qa
sqa is set
Class ((S,U1,U2,(S,F)),sqa) is Element of bool (S, the Sorts of U1,(S,F))
S1 is Element of bool (Class (S,U1,U2,(S,F)))
S1O is set
sqa is Element of qa
s1 is set
Class ((S,U1,U2,(S,F)),s1) is Element of bool (S, the Sorts of U1,(S,F))
sqa is set
Class ((S,U1,U2,(S,F)),sqa) is Element of bool (S, the Sorts of U1,(S,F))
sqa is set
Class ((S,U1,U2,(S,F)),sqa) is Element of bool (S, the Sorts of U1,(S,F))
s1 is set
Class ((S,U1,U2,(S,F)),s1) is Element of bool (S, the Sorts of U1,(S,F))
S1O is set
s1 is set
sqa is set
Class ((S,U1,U2,(S,F)),s1) is Element of bool (S, the Sorts of U1,(S,F))
R is Element of bool (Class (S,U1,U2,(S,F)))
mc is Element of bool (Class (S,U1,U2,(S,F)))
qa is set
qh is set
Class ((S,U1,U2,(S,F)),qh) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
qh is set
Class ((S,U1,U2,(S,F)),qh) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
F is Element of the carrier of S
(S,U1,U2,F) is Element of bool (Class (S,U1,U2,(S,F)))
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S, the Sorts of U1,(S,F)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
(S,U1,U2,(S,F)) is Relation-like (S, the Sorts of U1,(S,F)) -defined (S, the Sorts of U1,(S,F)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):]
[:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is non empty set
Class (S,U1,U2,(S,F)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,F))
bool (Class (S,U1,U2,(S,F))) is non empty set
the Sorts of U1 . F is non empty set
R is set
Class ((S,U1,U2,(S,F)),R) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is order-sorted MSAlgebra over S
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
F is Element of the carrier of S
R is Element of the carrier of S
(S,U1,U2,F) is Element of bool (Class (S,U1,U2,(S,F)))
the Sorts of U1 is non empty Relation-like the carrier of S -defined Function-like total set
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S, the Sorts of U1,(S,F)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
(S,U1,U2,(S,F)) is Relation-like (S, the Sorts of U1,(S,F)) -defined (S, the Sorts of U1,(S,F)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):]
[:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is non empty set
Class (S,U1,U2,(S,F)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,F))
bool (Class (S,U1,U2,(S,F))) is non empty set
(S,U1,U2,R) is Element of bool (Class (S,U1,U2,(S,R)))
(S,R) is non empty directed Element of (S)
Class ((S),R) is Element of bool the carrier of S
(S, the Sorts of U1,(S,R)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
(S,U1,U2,(S,R)) is Relation-like (S, the Sorts of U1,(S,R)) -defined (S, the Sorts of U1,(S,R)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):]
[:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is non empty set
Class (S,U1,U2,(S,R)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,R))
bool (Class (S,U1,U2,(S,R))) is non empty set
S1 is set
the Sorts of U1 . F is set
qh is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
mc is Element of the carrier of S
qh . mc is set
qa is Element of the carrier of S
qh . qa is set
S1O is set
Class ((S,U1,U2,(S,F)),S1O) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is order-sorted MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
the Sorts of U1 is non empty Relation-like the carrier of S -defined Function-like total set
F is Relation-like Function-like set
dom F is set
R is non empty Relation-like the carrier of S -defined Function-like total set
qa is Element of the carrier of S
qh is Element of the carrier of S
R . qa is set
R . qh is set
(S,U1,U2,qa) is Element of bool (Class (S,U1,U2,(S,qa)))
(S,qa) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),qa) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qa)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
(S,U1,U2,(S,qa)) is Relation-like (S, the Sorts of U1,(S,qa)) -defined (S, the Sorts of U1,(S,qa)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):]
[:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is non empty set
Class (S,U1,U2,(S,qa)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qa))
bool (Class (S,U1,U2,(S,qa))) is non empty set
(S,U1,U2,qh) is Element of bool (Class (S,U1,U2,(S,qh)))
(S,qh) is non empty directed Element of (S)
Class ((S),qh) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qh)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
(S,U1,U2,(S,qh)) is Relation-like (S, the Sorts of U1,(S,qh)) -defined (S, the Sorts of U1,(S,qh)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):]
[:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is non empty set
Class (S,U1,U2,(S,qh)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qh))
bool (Class (S,U1,U2,(S,qh))) is non empty set
F is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
R is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
mc is set
F . mc is set
qa is Element of the carrier of S
(S,U1,U2,qa) is Element of bool (Class (S,U1,U2,(S,qa)))
the Sorts of U1 is non empty Relation-like the carrier of S -defined Function-like total set
(S,qa) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),qa) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qa)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
(S,U1,U2,(S,qa)) is Relation-like (S, the Sorts of U1,(S,qa)) -defined (S, the Sorts of U1,(S,qa)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):]
[:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is non empty set
Class (S,U1,U2,(S,qa)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qa))
bool (Class (S,U1,U2,(S,qa))) is non empty set
R . mc is set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
(S,U1,U2) is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
F is set
(S,U1,U2) . F is set
R is Element of the carrier of S
(S,U1,U2) . R is set
(S,U1,U2,R) is non empty Element of bool (Class (S,U1,U2,(S,R)))
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
(S,R) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),R) is Element of bool the carrier of S
(S, the Sorts of U1,(S,R)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
(S,U1,U2,(S,R)) is Relation-like (S, the Sorts of U1,(S,R)) -defined (S, the Sorts of U1,(S,R)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):]
[:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is non empty set
Class (S,U1,U2,(S,R)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,R))
bool (Class (S,U1,U2,(S,R))) is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is Element of the carrier of S
the Sorts of U1 . F is non empty set
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S, the Sorts of U1,(S,F)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
(S,U1,U2,(S,F)) is Relation-like (S, the Sorts of U1,(S,F)) -defined (S, the Sorts of U1,(S,F)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):]
[:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is non empty set
R is Element of the Sorts of U1 . F
Class ((S,U1,U2,(S,F)),R) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
(S,U1,U2,F) is non empty Element of bool (Class (S,U1,U2,(S,F)))
Class (S,U1,U2,(S,F)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,F))
bool (Class (S,U1,U2,(S,F))) is non empty set
S is non empty reflexive transitive antisymmetric () RelStr
the carrier of S is non empty set
U1 is Element of the carrier of S
U2 is Element of the carrier of S
F is Element of the carrier of S
F is Element of the carrier of S
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S,U2) is non empty directed Element of (S)
Class ((S),U2) is Element of bool the carrier of S
(S,U1) is non empty directed Element of (S)
Class ((S),U1) is Element of bool the carrier of S
R is Element of the carrier of S
mc is Element of the carrier of S
qa is Element of the carrier of S
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
F is Element of the carrier of S
the Sorts of U1 . F is non empty set
U2 . F is Relation-like the Sorts of U1 . F -defined the Sorts of U1 . F -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . F),( the Sorts of U1 . F):]
[:( the Sorts of U1 . F),( the Sorts of U1 . F):] is non empty Relation-like set
bool [:( the Sorts of U1 . F),( the Sorts of U1 . F):] is non empty set
R is Element of the Sorts of U1 . F
(S,U1,U2,F,R) is Element of (S,U1,U2,F)
(S,U1,U2,F) is non empty Element of bool (Class (S,U1,U2,(S,F)))
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S, the Sorts of U1,(S,F)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
(S,U1,U2,(S,F)) is Relation-like (S, the Sorts of U1,(S,F)) -defined (S, the Sorts of U1,(S,F)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):]
[:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is non empty set
Class (S,U1,U2,(S,F)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,F))
bool (Class (S,U1,U2,(S,F))) is non empty set
Class ((S,U1,U2,(S,F)),R) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
mc is Element of the Sorts of U1 . F
(S,U1,U2,F,mc) is Element of (S,U1,U2,F)
Class ((S,U1,U2,(S,F)),mc) is Element of bool (S, the Sorts of U1,(S,F))
[R,mc] is set
{R,mc} is set
{R} is set
{{R,mc},{R}} is set
qh is Element of the carrier of S
U2 . qh is Relation-like the Sorts of U1 . qh -defined the Sorts of U1 . qh -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . qh),( the Sorts of U1 . qh):]
the Sorts of U1 . qh is non empty set
[:( the Sorts of U1 . qh),( the Sorts of U1 . qh):] is non empty Relation-like set
bool [:( the Sorts of U1 . qh),( the Sorts of U1 . qh):] is non empty set
S1O is Element of the carrier of S
S1 is Element of the carrier of S
sqa is Element of the carrier of S
qa is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
qa . S1O is set
U2 . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
the Sorts of U1 . sqa is non empty set
[:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty Relation-like set
bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is Element of the carrier of S
the Sorts of U1 . F is non empty set
R is Element of the carrier of S
the Sorts of U1 . R is non empty set
qa is Element of the Sorts of U1 . R
mc is Element of the Sorts of U1 . F
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
(S,U1,U2,F,mc) is Element of (S,U1,U2,F)
(S,U1,U2,F) is non empty Element of bool (Class (S,U1,U2,(S,F)))
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S, the Sorts of U1,(S,F)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
(S,U1,U2,(S,F)) is Relation-like (S, the Sorts of U1,(S,F)) -defined (S, the Sorts of U1,(S,F)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):]
[:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is non empty set
Class (S,U1,U2,(S,F)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,F))
bool (Class (S,U1,U2,(S,F))) is non empty set
Class ((S,U1,U2,(S,F)),mc) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
(S,U1,U2,R,qa) is Element of (S,U1,U2,R)
(S,U1,U2,R) is non empty Element of bool (Class (S,U1,U2,(S,R)))
(S,R) is non empty directed Element of (S)
Class ((S),R) is Element of bool the carrier of S
(S, the Sorts of U1,(S,R)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
(S,U1,U2,(S,R)) is Relation-like (S, the Sorts of U1,(S,R)) -defined (S, the Sorts of U1,(S,R)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):]
[:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is non empty set
Class (S,U1,U2,(S,R)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,R))
bool (Class (S,U1,U2,(S,R))) is non empty set
Class ((S,U1,U2,(S,R)),qa) is Element of bool (S, the Sorts of U1,(S,R))
bool (S, the Sorts of U1,(S,R)) is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier' of S is non empty set
U2 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
U1 is Element of the carrier' of S
Args (U1,U2) is non empty functional Element of rng ( the Sorts of U2 #)
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of U2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
rng ( the Sorts of U2 #) is non empty with_non-empty_elements set
the_arity_of U1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U2)
(S,U2,F) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(the_arity_of U1) * (S,U2,F) is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of U1) is countable Element of bool NAT
product ((the_arity_of U1) * (S,U2,F)) is non empty functional with_common_domain product-like set
R is Relation-like Function-like Element of Args (U1,U2)
qh is set
S1 is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of U1) /. S1 is Element of the carrier of S
the Sorts of U2 . ((the_arity_of U1) /. S1) is non empty set
R . S1 is set
S1O is Element of the Sorts of U2 . ((the_arity_of U1) /. S1)
(S,U2,F,((the_arity_of U1) /. S1),S1O) is Element of (S,U2,F,((the_arity_of U1) /. S1))
(S,U2,F,((the_arity_of U1) /. S1)) is non empty Element of bool (Class (S,U2,F,(S,((the_arity_of U1) /. S1))))
(S,((the_arity_of U1) /. S1)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),((the_arity_of U1) /. S1)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. S1)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. S1)) } is set
(S,U2,F,(S,((the_arity_of U1) /. S1))) is Relation-like (S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) -defined (S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))):]
[:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))):] is non empty set
Class (S,U2,F,(S,((the_arity_of U1) /. S1))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,((the_arity_of U1) /. S1)))
bool (Class (S,U2,F,(S,((the_arity_of U1) /. S1)))) is non empty set
Class ((S,U2,F,(S,((the_arity_of U1) /. S1))),S1O) is Element of bool (S, the Sorts of U2,(S,((the_arity_of U1) /. S1)))
bool (S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) is non empty set
sqa is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of U1) /. sqa is Element of the carrier of S
the Sorts of U2 . ((the_arity_of U1) /. sqa) is non empty set
R . sqa is set
qh is Relation-like Function-like set
dom qh is set
dom ((the_arity_of U1) * (S,U2,F)) is countable Element of bool NAT
S1 is set
qh . S1 is set
((the_arity_of U1) * (S,U2,F)) . S1 is set
(the_arity_of U1) . S1 is set
rng (the_arity_of U1) is Element of bool the carrier of S
bool the carrier of S is non empty set
S1O is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of U1) /. S1O is Element of the carrier of S
the Sorts of U2 . ((the_arity_of U1) /. S1O) is non empty set
R . S1O is set
qh . S1O is set
(the_arity_of U1) . S1O is set
sqa is Element of the carrier of S
(S,U2,F,sqa) is non empty Element of bool (Class (S,U2,F,(S,sqa)))
(S,sqa) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),sqa) is Element of bool the carrier of S
(S, the Sorts of U2,(S,sqa)) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,sqa) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,sqa) } is set
(S,U2,F,(S,sqa)) is Relation-like (S, the Sorts of U2,(S,sqa)) -defined (S, the Sorts of U2,(S,sqa)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,sqa)),(S, the Sorts of U2,(S,sqa)):]
[:(S, the Sorts of U2,(S,sqa)),(S, the Sorts of U2,(S,sqa)):] is Relation-like set
bool [:(S, the Sorts of U2,(S,sqa)),(S, the Sorts of U2,(S,sqa)):] is non empty set
Class (S,U2,F,(S,sqa)) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,sqa))
bool (Class (S,U2,F,(S,sqa))) is non empty set
s1 is Element of the Sorts of U2 . ((the_arity_of U1) /. S1O)
(S,U2,F,((the_arity_of U1) /. S1O),s1) is Element of (S,U2,F,((the_arity_of U1) /. S1O))
(S,U2,F,((the_arity_of U1) /. S1O)) is non empty Element of bool (Class (S,U2,F,(S,((the_arity_of U1) /. S1O))))
(S,((the_arity_of U1) /. S1O)) is non empty directed Element of (S)
Class ((S),((the_arity_of U1) /. S1O)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. S1O)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. S1O)) } is set
(S,U2,F,(S,((the_arity_of U1) /. S1O))) is Relation-like (S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))) -defined (S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))):]
[:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))):] is non empty set
Class (S,U2,F,(S,((the_arity_of U1) /. S1O))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,((the_arity_of U1) /. S1O)))
bool (Class (S,U2,F,(S,((the_arity_of U1) /. S1O)))) is non empty set
Class ((S,U2,F,(S,((the_arity_of U1) /. S1O))),s1) is Element of bool (S, the Sorts of U2,(S,((the_arity_of U1) /. S1O)))
bool (S, the Sorts of U2,(S,((the_arity_of U1) /. S1O))) is non empty set
(S,U2,F) . ((the_arity_of U1) . S1) is set
S1 is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
S1O is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of U1) /. S1O is Element of the carrier of S
the Sorts of U2 . ((the_arity_of U1) /. S1O) is non empty set
R . S1O is set
S1 . S1O is set
mc is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
qa is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
qh is set
mc . qh is set
qa . qh is set
S1 is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of U1) /. S1 is Element of the carrier of S
the Sorts of U2 . ((the_arity_of U1) /. S1) is non empty set
R . S1 is set
mc . S1 is set
qa . S1 is set
S1O is Element of the Sorts of U2 . ((the_arity_of U1) /. S1)
(S,U2,F,((the_arity_of U1) /. S1),S1O) is Element of (S,U2,F,((the_arity_of U1) /. S1))
(S,U2,F,((the_arity_of U1) /. S1)) is non empty Element of bool (Class (S,U2,F,(S,((the_arity_of U1) /. S1))))
(S,((the_arity_of U1) /. S1)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),((the_arity_of U1) /. S1)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. S1)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. S1)) } is set
(S,U2,F,(S,((the_arity_of U1) /. S1))) is Relation-like (S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) -defined (S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))):]
[:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))),(S, the Sorts of U2,(S,((the_arity_of U1) /. S1))):] is non empty set
Class (S,U2,F,(S,((the_arity_of U1) /. S1))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,((the_arity_of U1) /. S1)))
bool (Class (S,U2,F,(S,((the_arity_of U1) /. S1)))) is non empty set
Class ((S,U2,F,(S,((the_arity_of U1) /. S1))),S1O) is Element of bool (S, the Sorts of U2,(S,((the_arity_of U1) /. S1)))
bool (S, the Sorts of U2,(S,((the_arity_of U1) /. S1))) is non empty set
sqa is Element of the Sorts of U2 . ((the_arity_of U1) /. S1)
(S,U2,F,((the_arity_of U1) /. S1),sqa) is Element of (S,U2,F,((the_arity_of U1) /. S1))
Class ((S,U2,F,(S,((the_arity_of U1) /. S1))),sqa) is Element of bool (S, the Sorts of U2,(S,((the_arity_of U1) /. S1)))
dom qa is countable Element of bool NAT
dom mc is countable Element of bool NAT
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier' of S is non empty set
U2 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the ResultSort of S * the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
U1 is Element of the carrier' of S
( the ResultSort of S * the Sorts of U2) . U1 is non empty set
F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U2)
(S,U2,F) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
the ResultSort of S * (S,U2,F) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the ResultSort of S * (S,U2,F)) . U1 is non empty set
[:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty set
the_result_sort_of U1 is Element of the carrier of S
the Sorts of U2 . (the_result_sort_of U1) is non empty set
(S,U2,F,(the_result_sort_of U1)) is non empty Element of bool (Class (S,U2,F,(S,(the_result_sort_of U1))))
(S,(the_result_sort_of U1)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),(the_result_sort_of U1)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,(the_result_sort_of U1))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of U1)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of U1)) } is set
(S,U2,F,(S,(the_result_sort_of U1))) is Relation-like (S, the Sorts of U2,(S,(the_result_sort_of U1))) -defined (S, the Sorts of U2,(S,(the_result_sort_of U1))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):]
[:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):] is non empty set
Class (S,U2,F,(S,(the_result_sort_of U1))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,(the_result_sort_of U1)))
bool (Class (S,U2,F,(S,(the_result_sort_of U1)))) is non empty set
qa is Relation-like Function-like set
dom qa is set
(S,U2,F) . (the_result_sort_of U1) is non empty set
qh is set
qa . qh is set
S1 is Element of the Sorts of U2 . (the_result_sort_of U1)
qa . S1 is set
(S,U2,F,(the_result_sort_of U1),S1) is Element of (S,U2,F,(the_result_sort_of U1))
Class ((S,U2,F,(S,(the_result_sort_of U1))),S1) is Element of bool (S, the Sorts of U2,(S,(the_result_sort_of U1)))
bool (S, the Sorts of U2,(S,(the_result_sort_of U1))) is non empty set
dom ( the ResultSort of S * the Sorts of U2) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
the ResultSort of S . U1 is Element of the carrier of S
the Sorts of U2 . ( the ResultSort of S . U1) is non empty set
dom the ResultSort of S is Element of bool the carrier' of S
dom ( the ResultSort of S * (S,U2,F)) is non empty Element of bool the carrier' of S
(S,U2,F) . ( the ResultSort of S . U1) is non empty set
qh is Relation-like ( the ResultSort of S * the Sorts of U2) . U1 -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like V30(( the ResultSort of S * the Sorts of U2) . U1,( the ResultSort of S * (S,U2,F)) . U1) Element of bool [:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):]
S1 is Element of the Sorts of U2 . (the_result_sort_of U1)
qh . S1 is set
(S,U2,F,(the_result_sort_of U1),S1) is Element of (S,U2,F,(the_result_sort_of U1))
Class ((S,U2,F,(S,(the_result_sort_of U1))),S1) is Element of bool (S, the Sorts of U2,(S,(the_result_sort_of U1)))
bool (S, the Sorts of U2,(S,(the_result_sort_of U1))) is non empty set
qh is Relation-like ( the ResultSort of S * the Sorts of U2) . U1 -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like V30(( the ResultSort of S * the Sorts of U2) . U1,( the ResultSort of S * (S,U2,F)) . U1) Element of bool [:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):]
S1 is Relation-like ( the ResultSort of S * the Sorts of U2) . U1 -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like V30(( the ResultSort of S * the Sorts of U2) . U1,( the ResultSort of S * (S,U2,F)) . U1) Element of bool [:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):]
S1O is set
sqa is Element of the Sorts of U2 . (the_result_sort_of U1)
qh . sqa is set
(S,U2,F,(the_result_sort_of U1),sqa) is Element of (S,U2,F,(the_result_sort_of U1))
(S,U2,F,(the_result_sort_of U1)) is non empty Element of bool (Class (S,U2,F,(S,(the_result_sort_of U1))))
(S,(the_result_sort_of U1)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),(the_result_sort_of U1)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,(the_result_sort_of U1))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of U1)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of U1)) } is set
(S,U2,F,(S,(the_result_sort_of U1))) is Relation-like (S, the Sorts of U2,(S,(the_result_sort_of U1))) -defined (S, the Sorts of U2,(S,(the_result_sort_of U1))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):]
[:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):] is non empty set
Class (S,U2,F,(S,(the_result_sort_of U1))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,(the_result_sort_of U1)))
bool (Class (S,U2,F,(S,(the_result_sort_of U1)))) is non empty set
Class ((S,U2,F,(S,(the_result_sort_of U1))),sqa) is Element of bool (S, the Sorts of U2,(S,(the_result_sort_of U1)))
bool (S, the Sorts of U2,(S,(the_result_sort_of U1))) is non empty set
qh . S1O is set
S1 . S1O is set
dom ( the ResultSort of S * the Sorts of U2) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
the ResultSort of S . U1 is Element of the carrier of S
the Sorts of U2 . ( the ResultSort of S . U1) is non empty set
dom qh is Element of bool (( the ResultSort of S * the Sorts of U2) . U1)
bool (( the ResultSort of S * the Sorts of U2) . U1) is non empty set
dom S1 is Element of bool (( the ResultSort of S * the Sorts of U2) . U1)
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
the Sorts of U2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of U2 #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the Arity of S * ( the Sorts of U2 #)) . U1 is non empty set
(S,U2,F) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U2,F) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the Arity of S * ((S,U2,F) #)) . U1 is non empty set
[:(( the Arity of S * ( the Sorts of U2 #)) . U1),(( the Arity of S * ((S,U2,F) #)) . U1):] is non empty Relation-like set
bool [:(( the Arity of S * ( the Sorts of U2 #)) . U1),(( the Arity of S * ((S,U2,F) #)) . U1):] is non empty set
Args (U1,U2) is non empty functional Element of rng ( the Sorts of U2 #)
rng ( the Sorts of U2 #) is non empty with_non-empty_elements set
the_arity_of U1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(the_arity_of U1) * (S,U2,F) is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of U1) is countable Element of bool NAT
product ((the_arity_of U1) * (S,U2,F)) is non empty functional with_common_domain product-like set
qa is Relation-like Function-like set
dom qa is set
dom ( the Arity of S * ( the Sorts of U2 #)) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
the Arity of S . U1 is Relation-like NAT -defined Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
( the Sorts of U2 #) . ( the Arity of S . U1) is non empty set
( the Sorts of U2 #) . (the_arity_of U1) is non empty set
((S,U2,F) #) . (the_arity_of U1) is non empty set
qh is set
qa . qh is set
S1 is Relation-like Function-like Element of Args (U1,U2)
qa . S1 is set
(S,U1,U2,F,S1) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
dom ( the Arity of S * ((S,U2,F) #)) is non empty Element of bool the carrier' of S
((S,U2,F) #) . ( the Arity of S . U1) is non empty set
qh is Relation-like ( the Arity of S * ( the Sorts of U2 #)) . U1 -defined ( the Arity of S * ((S,U2,F) #)) . U1 -valued Function-like V30(( the Arity of S * ( the Sorts of U2 #)) . U1,( the Arity of S * ((S,U2,F) #)) . U1) Element of bool [:(( the Arity of S * ( the Sorts of U2 #)) . U1),(( the Arity of S * ((S,U2,F) #)) . U1):]
S1 is Relation-like Function-like Element of Args (U1,U2)
qh . S1 is set
(S,U1,U2,F,S1) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
the_arity_of U1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
mc is Relation-like ( the Arity of S * ( the Sorts of U2 #)) . U1 -defined ( the Arity of S * ((S,U2,F) #)) . U1 -valued Function-like V30(( the Arity of S * ( the Sorts of U2 #)) . U1,( the Arity of S * ((S,U2,F) #)) . U1) Element of bool [:(( the Arity of S * ( the Sorts of U2 #)) . U1),(( the Arity of S * ((S,U2,F) #)) . U1):]
qa is Relation-like ( the Arity of S * ( the Sorts of U2 #)) . U1 -defined ( the Arity of S * ((S,U2,F) #)) . U1 -valued Function-like V30(( the Arity of S * ( the Sorts of U2 #)) . U1,( the Arity of S * ((S,U2,F) #)) . U1) Element of bool [:(( the Arity of S * ( the Sorts of U2 #)) . U1),(( the Arity of S * ((S,U2,F) #)) . U1):]
dom ( the Arity of S * ( the Sorts of U2 #)) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
the Arity of S . U1 is Relation-like NAT -defined Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
( the Sorts of U2 #) . ( the Arity of S . U1) is non empty set
( the Sorts of U2 #) . (the_arity_of U1) is non empty set
qh is set
S1 is Relation-like Function-like Element of Args (U1,U2)
mc . S1 is set
(S,U1,U2,F,S1) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
(the_arity_of U1) * (S,U2,F) is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of U1) is countable Element of bool NAT
product ((the_arity_of U1) * (S,U2,F)) is non empty functional with_common_domain product-like set
mc . qh is set
qa . qh is set
dom mc is Element of bool (( the Arity of S * ( the Sorts of U2 #)) . U1)
bool (( the Arity of S * ( the Sorts of U2 #)) . U1) is non empty set
dom qa is Element of bool (( the Arity of S * ( the Sorts of U2 #)) . U1)
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the carrier' of S is non empty set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the ResultSort of S * the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
the ResultSort of S * (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
R is set
mc is Element of the carrier' of S
(S,mc,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . mc -defined ( the ResultSort of S * (S,U1,U2)) . mc -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . mc,( the ResultSort of S * (S,U1,U2)) . mc) Element of bool [:(( the ResultSort of S * the Sorts of U1) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):]
( the ResultSort of S * the Sorts of U1) . mc is non empty set
( the ResultSort of S * (S,U1,U2)) . mc is non empty set
[:(( the ResultSort of S * the Sorts of U1) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty set
qa is Element of the carrier' of S
(S,qa,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
( the ResultSort of S * the Sorts of U1) . qa is non empty set
( the ResultSort of S * (S,U1,U2)) . qa is non empty set
[:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
R is Relation-like Function-like set
dom R is set
mc is non empty Relation-like the carrier' of S -defined Function-like total set
dom mc is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
qa is set
mc . qa is set
qh is Element of the carrier' of S
mc . qh is set
(S,qh,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . qh -defined ( the ResultSort of S * (S,U1,U2)) . qh -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . qh,( the ResultSort of S * (S,U1,U2)) . qh) Element of bool [:(( the ResultSort of S * the Sorts of U1) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):]
( the ResultSort of S * the Sorts of U1) . qh is non empty set
( the ResultSort of S * (S,U1,U2)) . qh is non empty set
[:(( the ResultSort of S * the Sorts of U1) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is non empty set
qa is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding set
qh is set
qa . qh is Relation-like Function-like set
( the ResultSort of S * the Sorts of U1) . qh is set
( the ResultSort of S * (S,U1,U2)) . qh is set
[:(( the ResultSort of S * the Sorts of U1) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is non empty set
S1 is Element of the carrier' of S
qa . S1 is Relation-like Function-like set
(S,S1,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . S1 -defined ( the ResultSort of S * (S,U1,U2)) . S1 -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . S1,( the ResultSort of S * (S,U1,U2)) . S1) Element of bool [:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):]
( the ResultSort of S * the Sorts of U1) . S1 is non empty set
( the ResultSort of S * (S,U1,U2)) . S1 is non empty set
[:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty set
qh is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the ResultSort of S * the Sorts of U1, the ResultSort of S * (S,U1,U2)
S1 is Element of the carrier' of S
( the ResultSort of S * the Sorts of U1) . S1 is non empty set
( the ResultSort of S * (S,U1,U2)) . S1 is non empty set
qh . S1 is Relation-like ( the ResultSort of S * the Sorts of U1) . S1 -defined ( the ResultSort of S * (S,U1,U2)) . S1 -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . S1,( the ResultSort of S * (S,U1,U2)) . S1) Element of bool [:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):]
[:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty set
(S,S1,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . S1 -defined ( the ResultSort of S * (S,U1,U2)) . S1 -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . S1,( the ResultSort of S * (S,U1,U2)) . S1) Element of bool [:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):]
F is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the ResultSort of S * the Sorts of U1, the ResultSort of S * (S,U1,U2)
R is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the ResultSort of S * the Sorts of U1, the ResultSort of S * (S,U1,U2)
mc is set
qa is Element of the carrier' of S
( the ResultSort of S * the Sorts of U1) . qa is non empty set
( the ResultSort of S * (S,U1,U2)) . qa is non empty set
F . qa is Relation-like ( the ResultSort of S * the Sorts of U1) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
[:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
(S,qa,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
F . mc is Relation-like Function-like set
R . mc is Relation-like Function-like set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ( the Sorts of U1 #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
(S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,U2) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
R is set
mc is Element of the carrier' of S
(S,mc,U1,U2) is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . mc -defined ( the Arity of S * ((S,U1,U2) #)) . mc -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . mc,( the Arity of S * ((S,U1,U2) #)) . mc) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . mc),(( the Arity of S * ((S,U1,U2) #)) . mc):]
( the Arity of S * ( the Sorts of U1 #)) . mc is non empty set
( the Arity of S * ((S,U1,U2) #)) . mc is non empty set
[:(( the Arity of S * ( the Sorts of U1 #)) . mc),(( the Arity of S * ((S,U1,U2) #)) . mc):] is non empty Relation-like set
bool [:(( the Arity of S * ( the Sorts of U1 #)) . mc),(( the Arity of S * ((S,U1,U2) #)) . mc):] is non empty set
qa is Element of the carrier' of S
(S,qa,U1,U2) is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . qa -defined ( the Arity of S * ((S,U1,U2) #)) . qa -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . qa,( the Arity of S * ((S,U1,U2) #)) . qa) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . qa),(( the Arity of S * ((S,U1,U2) #)) . qa):]
( the Arity of S * ( the Sorts of U1 #)) . qa is non empty set
( the Arity of S * ((S,U1,U2) #)) . qa is non empty set
[:(( the Arity of S * ( the Sorts of U1 #)) . qa),(( the Arity of S * ((S,U1,U2) #)) . qa):] is non empty Relation-like set
bool [:(( the Arity of S * ( the Sorts of U1 #)) . qa),(( the Arity of S * ((S,U1,U2) #)) . qa):] is non empty set
R is Relation-like Function-like set
dom R is set
mc is non empty Relation-like the carrier' of S -defined Function-like total set
dom mc is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
qa is set
mc . qa is set
qh is Element of the carrier' of S
mc . qh is set
(S,qh,U1,U2) is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . qh -defined ( the Arity of S * ((S,U1,U2) #)) . qh -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . qh,( the Arity of S * ((S,U1,U2) #)) . qh) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . qh),(( the Arity of S * ((S,U1,U2) #)) . qh):]
( the Arity of S * ( the Sorts of U1 #)) . qh is non empty set
( the Arity of S * ((S,U1,U2) #)) . qh is non empty set
[:(( the Arity of S * ( the Sorts of U1 #)) . qh),(( the Arity of S * ((S,U1,U2) #)) . qh):] is non empty Relation-like set
bool [:(( the Arity of S * ( the Sorts of U1 #)) . qh),(( the Arity of S * ((S,U1,U2) #)) . qh):] is non empty set
qa is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding set
qh is set
qa . qh is Relation-like Function-like set
( the Arity of S * ( the Sorts of U1 #)) . qh is set
( the Arity of S * ((S,U1,U2) #)) . qh is set
[:(( the Arity of S * ( the Sorts of U1 #)) . qh),(( the Arity of S * ((S,U1,U2) #)) . qh):] is Relation-like set
bool [:(( the Arity of S * ( the Sorts of U1 #)) . qh),(( the Arity of S * ((S,U1,U2) #)) . qh):] is non empty set
S1 is Element of the carrier' of S
qa . S1 is Relation-like Function-like set
(S,S1,U1,U2) is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . S1 -defined ( the Arity of S * ((S,U1,U2) #)) . S1 -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . S1,( the Arity of S * ((S,U1,U2) #)) . S1) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . S1),(( the Arity of S * ((S,U1,U2) #)) . S1):]
( the Arity of S * ( the Sorts of U1 #)) . S1 is non empty set
( the Arity of S * ((S,U1,U2) #)) . S1 is non empty set
[:(( the Arity of S * ( the Sorts of U1 #)) . S1),(( the Arity of S * ((S,U1,U2) #)) . S1):] is non empty Relation-like set
bool [:(( the Arity of S * ( the Sorts of U1 #)) . S1),(( the Arity of S * ((S,U1,U2) #)) . S1):] is non empty set
qh is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ( the Sorts of U1 #), the Arity of S * ((S,U1,U2) #)
S1 is Element of the carrier' of S
( the Arity of S * ( the Sorts of U1 #)) . S1 is non empty set
( the Arity of S * ((S,U1,U2) #)) . S1 is non empty set
qh . S1 is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . S1 -defined ( the Arity of S * ((S,U1,U2) #)) . S1 -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . S1,( the Arity of S * ((S,U1,U2) #)) . S1) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . S1),(( the Arity of S * ((S,U1,U2) #)) . S1):]
[:(( the Arity of S * ( the Sorts of U1 #)) . S1),(( the Arity of S * ((S,U1,U2) #)) . S1):] is non empty Relation-like set
bool [:(( the Arity of S * ( the Sorts of U1 #)) . S1),(( the Arity of S * ((S,U1,U2) #)) . S1):] is non empty set
(S,S1,U1,U2) is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . S1 -defined ( the Arity of S * ((S,U1,U2) #)) . S1 -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . S1,( the Arity of S * ((S,U1,U2) #)) . S1) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . S1),(( the Arity of S * ((S,U1,U2) #)) . S1):]
F is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ( the Sorts of U1 #), the Arity of S * ((S,U1,U2) #)
R is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ( the Sorts of U1 #), the Arity of S * ((S,U1,U2) #)
mc is set
qa is Element of the carrier' of S
( the Arity of S * ( the Sorts of U1 #)) . qa is non empty set
( the Arity of S * ((S,U1,U2) #)) . qa is non empty set
F . qa is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . qa -defined ( the Arity of S * ((S,U1,U2) #)) . qa -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . qa,( the Arity of S * ((S,U1,U2) #)) . qa) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . qa),(( the Arity of S * ((S,U1,U2) #)) . qa):]
[:(( the Arity of S * ( the Sorts of U1 #)) . qa),(( the Arity of S * ((S,U1,U2) #)) . qa):] is non empty Relation-like set
bool [:(( the Arity of S * ( the Sorts of U1 #)) . qa),(( the Arity of S * ((S,U1,U2) #)) . qa):] is non empty set
(S,qa,U1,U2) is Relation-like ( the Arity of S * ( the Sorts of U1 #)) . qa -defined ( the Arity of S * ((S,U1,U2) #)) . qa -valued Function-like V30(( the Arity of S * ( the Sorts of U1 #)) . qa,( the Arity of S * ((S,U1,U2) #)) . qa) Element of bool [:(( the Arity of S * ( the Sorts of U1 #)) . qa),(( the Arity of S * ((S,U1,U2) #)) . qa):]
F . mc is Relation-like Function-like set
R . mc is Relation-like Function-like set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier' of S is non empty set
the carrier of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
U1 is Element of the carrier' of S
U2 is non-empty order-sorted MSAlgebra over S
Args (U1,U2) is non empty functional Element of rng ( the Sorts of U2 #)
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of U2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U2 #) is non empty with_non-empty_elements set
F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U2)
(S,U2,F) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U2,F) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U2,F) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the Arity of S * ((S,U2,F) #)) . U1 is non empty set
R is set
the_arity_of U1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the Arity of S . U1 is Relation-like NAT -defined Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(the_arity_of U1) * (S,U2,F) is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of U1) is countable Element of bool NAT
product ((the_arity_of U1) * (S,U2,F)) is non empty functional with_common_domain product-like set
dom ((the_arity_of U1) * (S,U2,F)) is countable Element of bool NAT
qa is Relation-like Function-like set
dom qa is set
qh is V4() V5() V6() V10() V11() V12() ext-real V33() set
qa . qh is set
(the_arity_of U1) /. qh is Element of the carrier of S
(S,U2,F,((the_arity_of U1) /. qh)) is non empty Element of bool (Class (S,U2,F,(S,((the_arity_of U1) /. qh))))
(S,((the_arity_of U1) /. qh)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),((the_arity_of U1) /. qh)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,((the_arity_of U1) /. qh))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. qh)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. qh)) } is set
(S,U2,F,(S,((the_arity_of U1) /. qh))) is Relation-like (S, the Sorts of U2,(S,((the_arity_of U1) /. qh))) -defined (S, the Sorts of U2,(S,((the_arity_of U1) /. qh))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. qh))),(S, the Sorts of U2,(S,((the_arity_of U1) /. qh))):]
[:(S, the Sorts of U2,(S,((the_arity_of U1) /. qh))),(S, the Sorts of U2,(S,((the_arity_of U1) /. qh))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. qh))),(S, the Sorts of U2,(S,((the_arity_of U1) /. qh))):] is non empty set
Class (S,U2,F,(S,((the_arity_of U1) /. qh))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,((the_arity_of U1) /. qh)))
bool (Class (S,U2,F,(S,((the_arity_of U1) /. qh)))) is non empty set
(the_arity_of U1) . qh is set
((the_arity_of U1) * (S,U2,F)) . qh is set
S1 is Element of the carrier of S
(S,U2,F) . S1 is non empty set
(S,U2,F,S1) is non empty Element of bool (Class (S,U2,F,(S,S1)))
(S,S1) is non empty directed Element of (S)
Class ((S),S1) is Element of bool the carrier of S
(S, the Sorts of U2,(S,S1)) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
(S,U2,F,(S,S1)) is Relation-like (S, the Sorts of U2,(S,S1)) -defined (S, the Sorts of U2,(S,S1)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,S1)),(S, the Sorts of U2,(S,S1)):]
[:(S, the Sorts of U2,(S,S1)),(S, the Sorts of U2,(S,S1)):] is Relation-like set
bool [:(S, the Sorts of U2,(S,S1)),(S, the Sorts of U2,(S,S1)):] is non empty set
Class (S,U2,F,(S,S1)) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,S1))
bool (Class (S,U2,F,(S,S1))) is non empty set
qh is set
(the_arity_of U1) /. qh is Element of the carrier of S
the Sorts of U2 . ((the_arity_of U1) /. qh) is non empty set
qa . qh is set
S1O is V4() V5() V6() V10() V11() V12() ext-real V33() set
qa . S1O is set
S1 is Element of the carrier of S
(S,U2,F,S1) is non empty Element of bool (Class (S,U2,F,(S,S1)))
(S,S1) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),S1) is Element of bool the carrier of S
(S, the Sorts of U2,(S,S1)) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
(S,U2,F,(S,S1)) is Relation-like (S, the Sorts of U2,(S,S1)) -defined (S, the Sorts of U2,(S,S1)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,S1)),(S, the Sorts of U2,(S,S1)):]
[:(S, the Sorts of U2,(S,S1)),(S, the Sorts of U2,(S,S1)):] is Relation-like set
bool [:(S, the Sorts of U2,(S,S1)),(S, the Sorts of U2,(S,S1)):] is non empty set
Class (S,U2,F,(S,S1)) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,S1))
bool (Class (S,U2,F,(S,S1))) is non empty set
the Sorts of U2 . S1 is non empty set
sqa is set
Class ((S,U2,F,(S,S1)),sqa) is Element of bool (S, the Sorts of U2,(S,S1))
bool (S, the Sorts of U2,(S,S1)) is non empty set
qh is Relation-like Function-like set
dom qh is set
dom the Sorts of U2 is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
rng (the_arity_of U1) is Element of bool the carrier of S
(the_arity_of U1) * the Sorts of U2 is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom ((the_arity_of U1) * the Sorts of U2) is countable Element of bool NAT
S1 is set
qh . S1 is set
((the_arity_of U1) * the Sorts of U2) . S1 is set
S1O is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of U1) /. S1O is Element of the carrier of S
(the_arity_of U1) . S1O is set
qh . S1O is set
sqa is Element of the carrier of S
the Sorts of U2 . sqa is non empty set
the Arity of S * ( the Sorts of U2 #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the Arity of S * ( the Sorts of U2 #)) . U1 is non empty set
product ((the_arity_of U1) * the Sorts of U2) is non empty functional with_common_domain product-like set
S1 is Relation-like Function-like Element of Args (U1,U2)
(S,U1,U2,F,S1) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
S1O is set
qa . S1O is set
(S,U1,U2,F,S1) . S1O is set
sqa is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of U1) /. sqa is Element of the carrier of S
the Sorts of U2 . ((the_arity_of U1) /. sqa) is non empty set
S1 . sqa is set
(S,U1,U2,F,S1) . sqa is set
qa . sqa is set
s1 is Element of the carrier of S
(S,U2,F,s1) is non empty Element of bool (Class (S,U2,F,(S,s1)))
(S,s1) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),s1) is Element of bool the carrier of S
(S, the Sorts of U2,(S,s1)) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s1) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s1) } is set
(S,U2,F,(S,s1)) is Relation-like (S, the Sorts of U2,(S,s1)) -defined (S, the Sorts of U2,(S,s1)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,s1)),(S, the Sorts of U2,(S,s1)):]
[:(S, the Sorts of U2,(S,s1)),(S, the Sorts of U2,(S,s1)):] is Relation-like set
bool [:(S, the Sorts of U2,(S,s1)),(S, the Sorts of U2,(S,s1)):] is non empty set
Class (S,U2,F,(S,s1)) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,s1))
bool (Class (S,U2,F,(S,s1))) is non empty set
the Sorts of U2 . s1 is non empty set
s2 is set
Class ((S,U2,F,(S,s1)),s2) is Element of bool (S, the Sorts of U2,(S,s1))
bool (S, the Sorts of U2,(S,s1)) is non empty set
a1 is Element of the Sorts of U2 . ((the_arity_of U1) /. sqa)
(S,U2,F,((the_arity_of U1) /. sqa),a1) is Element of (S,U2,F,((the_arity_of U1) /. sqa))
(S,U2,F,((the_arity_of U1) /. sqa)) is non empty Element of bool (Class (S,U2,F,(S,((the_arity_of U1) /. sqa))))
(S,((the_arity_of U1) /. sqa)) is non empty directed Element of (S)
Class ((S),((the_arity_of U1) /. sqa)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. sqa)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. sqa)) } is set
(S,U2,F,(S,((the_arity_of U1) /. sqa))) is Relation-like (S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))) -defined (S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))),(S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))):]
[:(S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))),(S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))),(S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))):] is non empty set
Class (S,U2,F,(S,((the_arity_of U1) /. sqa))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,((the_arity_of U1) /. sqa)))
bool (Class (S,U2,F,(S,((the_arity_of U1) /. sqa)))) is non empty set
Class ((S,U2,F,(S,((the_arity_of U1) /. sqa))),a1) is Element of bool (S, the Sorts of U2,(S,((the_arity_of U1) /. sqa)))
bool (S, the Sorts of U2,(S,((the_arity_of U1) /. sqa))) is non empty set
dom (S,U1,U2,F,S1) is countable Element of bool NAT
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier' of S is non empty set
U2 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U2)
(S,U2,F) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U2,F) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U2,F) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
U1 is Element of the carrier' of S
( the Arity of S * ((S,U2,F) #)) . U1 is non empty set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U2,F) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the ResultSort of S * (S,U2,F)) . U1 is non empty set
[:(( the Arity of S * ((S,U2,F) #)) . U1),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U2,F) #)) . U1),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty set
Args (U1,U2) is non empty functional Element of rng ( the Sorts of U2 #)
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of U2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U2 #) is non empty with_non-empty_elements set
Result (U1,U2) is non empty Element of rng the Sorts of U2
rng the Sorts of U2 is non empty with_non-empty_elements set
the ResultSort of S * the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the ResultSort of S * the Sorts of U2) . U1 is non empty set
Den (U1,U2) is Relation-like Args (U1,U2) -defined Result (U1,U2) -valued Function-like V30( Args (U1,U2), Result (U1,U2)) Element of bool [:(Args (U1,U2)),(Result (U1,U2)):]
[:(Args (U1,U2)),(Result (U1,U2)):] is non empty Relation-like set
bool [:(Args (U1,U2)),(Result (U1,U2)):] is non empty set
(S,U1,U2,F) is Relation-like ( the ResultSort of S * the Sorts of U2) . U1 -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like V30(( the ResultSort of S * the Sorts of U2) . U1,( the ResultSort of S * (S,U2,F)) . U1) Element of bool [:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):]
[:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U2) . U1),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty set
(S,U1,U2,F) * (Den (U1,U2)) is Relation-like Args (U1,U2) -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like Element of bool [:(Args (U1,U2)),(( the ResultSort of S * (S,U2,F)) . U1):]
[:(Args (U1,U2)),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty Relation-like set
bool [:(Args (U1,U2)),(( the ResultSort of S * (S,U2,F)) . U1):] is non empty set
the_result_sort_of U1 is Element of the carrier of S
the_arity_of U1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
S1 is set
S1O is Relation-like Function-like Element of Args (U1,U2)
(S,U1,U2,F,S1O) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
(the_arity_of U1) * (S,U2,F) is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of U1) is countable Element of bool NAT
product ((the_arity_of U1) * (S,U2,F)) is non empty functional with_common_domain product-like set
((S,U1,U2,F) * (Den (U1,U2))) . S1O is set
sqa is set
dom ( the ResultSort of S * (S,U2,F)) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
the ResultSort of S . U1 is Element of the carrier of S
(S,U2,F) . ( the ResultSort of S . U1) is non empty set
(S,U2,F) . (the_result_sort_of U1) is non empty set
dom ( the ResultSort of S * the Sorts of U2) is non empty Element of bool the carrier' of S
the Sorts of U2 . ( the ResultSort of S . U1) is non empty set
the Sorts of U2 . (the_result_sort_of U1) is non empty set
dom (S,U1,U2,F) is Element of bool (( the ResultSort of S * the Sorts of U2) . U1)
bool (( the ResultSort of S * the Sorts of U2) . U1) is non empty set
rng (Den (U1,U2)) is Element of bool (Result (U1,U2))
bool (Result (U1,U2)) is non empty set
dom (Den (U1,U2)) is functional Element of bool (Args (U1,U2))
bool (Args (U1,U2)) is non empty set
dom ((S,U1,U2,F) * (Den (U1,U2))) is functional Element of bool (Args (U1,U2))
(Den (U1,U2)) . S1O is Element of Result (U1,U2)
(S,U1,U2,F) . ((Den (U1,U2)) . S1O) is set
rng (S,U1,U2,F) is Element of bool (( the ResultSort of S * (S,U2,F)) . U1)
bool (( the ResultSort of S * (S,U2,F)) . U1) is non empty set
s1 is Relation-like Function-like Element of Args (U1,U2)
(S,U1,U2,F,s1) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
((S,U1,U2,F) * (Den (U1,U2))) . s1 is set
(Den (U1,U2)) . s1 is Element of Result (U1,U2)
a1 is Element of the Sorts of U2 . (the_result_sort_of U1)
(S,U1,U2,F) . a1 is set
(S,U2,F,(the_result_sort_of U1),a1) is Element of (S,U2,F,(the_result_sort_of U1))
(S,U2,F,(the_result_sort_of U1)) is non empty Element of bool (Class (S,U2,F,(S,(the_result_sort_of U1))))
(S,(the_result_sort_of U1)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),(the_result_sort_of U1)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,(the_result_sort_of U1))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of U1)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of U1)) } is set
(S,U2,F,(S,(the_result_sort_of U1))) is Relation-like (S, the Sorts of U2,(S,(the_result_sort_of U1))) -defined (S, the Sorts of U2,(S,(the_result_sort_of U1))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):]
[:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,(the_result_sort_of U1))),(S, the Sorts of U2,(S,(the_result_sort_of U1))):] is non empty set
Class (S,U2,F,(S,(the_result_sort_of U1))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,(the_result_sort_of U1)))
bool (Class (S,U2,F,(S,(the_result_sort_of U1)))) is non empty set
Class ((S,U2,F,(S,(the_result_sort_of U1))),a1) is Element of bool (S, the Sorts of U2,(S,(the_result_sort_of U1)))
bool (S, the Sorts of U2,(S,(the_result_sort_of U1))) is non empty set
dom S1O is set
x is V4() V5() V6() V10() V11() V12() ext-real V33() set
S1O . x is set
s1 . x is set
[(S1O . x),(s1 . x)] is set
{(S1O . x),(s1 . x)} is set
{(S1O . x)} is set
{{(S1O . x),(s1 . x)},{(S1O . x)}} is set
(the_arity_of U1) /. x is Element of the carrier of S
F . ((the_arity_of U1) /. x) is Relation-like the Sorts of U2 . ((the_arity_of U1) /. x) -defined the Sorts of U2 . ((the_arity_of U1) /. x) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U2 . ((the_arity_of U1) /. x)),( the Sorts of U2 . ((the_arity_of U1) /. x)):]
the Sorts of U2 . ((the_arity_of U1) /. x) is non empty set
[:( the Sorts of U2 . ((the_arity_of U1) /. x)),( the Sorts of U2 . ((the_arity_of U1) /. x)):] is non empty Relation-like set
bool [:( the Sorts of U2 . ((the_arity_of U1) /. x)),( the Sorts of U2 . ((the_arity_of U1) /. x)):] is non empty set
(S,U1,U2,F,S1O) . x is set
(S,U1,U2,F,s1) . x is set
x2 is Element of the Sorts of U2 . ((the_arity_of U1) /. x)
(S,U2,F,((the_arity_of U1) /. x),x2) is Element of (S,U2,F,((the_arity_of U1) /. x))
(S,U2,F,((the_arity_of U1) /. x)) is non empty Element of bool (Class (S,U2,F,(S,((the_arity_of U1) /. x))))
(S,((the_arity_of U1) /. x)) is non empty directed Element of (S)
Class ((S),((the_arity_of U1) /. x)) is Element of bool the carrier of S
(S, the Sorts of U2,(S,((the_arity_of U1) /. x))) is set
{ ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. x)) } is set
union { ( the Sorts of U2 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of U1) /. x)) } is set
(S,U2,F,(S,((the_arity_of U1) /. x))) is Relation-like (S, the Sorts of U2,(S,((the_arity_of U1) /. x))) -defined (S, the Sorts of U2,(S,((the_arity_of U1) /. x))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. x))),(S, the Sorts of U2,(S,((the_arity_of U1) /. x))):]
[:(S, the Sorts of U2,(S,((the_arity_of U1) /. x))),(S, the Sorts of U2,(S,((the_arity_of U1) /. x))):] is Relation-like set
bool [:(S, the Sorts of U2,(S,((the_arity_of U1) /. x))),(S, the Sorts of U2,(S,((the_arity_of U1) /. x))):] is non empty set
Class (S,U2,F,(S,((the_arity_of U1) /. x))) is with_non-empty_elements a_partition of (S, the Sorts of U2,(S,((the_arity_of U1) /. x)))
bool (Class (S,U2,F,(S,((the_arity_of U1) /. x)))) is non empty set
Class ((S,U2,F,(S,((the_arity_of U1) /. x))),x2) is Element of bool (S, the Sorts of U2,(S,((the_arity_of U1) /. x)))
bool (S, the Sorts of U2,(S,((the_arity_of U1) /. x))) is non empty set
s3 is Element of the Sorts of U2 . ((the_arity_of U1) /. x)
(S,U2,F,((the_arity_of U1) /. x),s3) is Element of (S,U2,F,((the_arity_of U1) /. x))
Class ((S,U2,F,(S,((the_arity_of U1) /. x))),s3) is Element of bool (S, the Sorts of U2,(S,((the_arity_of U1) /. x)))
s2 is Element of the Sorts of U2 . (the_result_sort_of U1)
[s2,a1] is set
{s2,a1} is set
{s2} is set
{{s2,a1},{s2}} is set
F . (the_result_sort_of U1) is Relation-like the Sorts of U2 . (the_result_sort_of U1) -defined the Sorts of U2 . (the_result_sort_of U1) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U2 . (the_result_sort_of U1)),( the Sorts of U2 . (the_result_sort_of U1)):]
[:( the Sorts of U2 . (the_result_sort_of U1)),( the Sorts of U2 . (the_result_sort_of U1)):] is non empty Relation-like set
bool [:( the Sorts of U2 . (the_result_sort_of U1)),( the Sorts of U2 . (the_result_sort_of U1)):] is non empty set
(S,U2,F,(the_result_sort_of U1),s2) is Element of (S,U2,F,(the_result_sort_of U1))
Class ((S,U2,F,(S,(the_result_sort_of U1))),s2) is Element of bool (S, the Sorts of U2,(S,(the_result_sort_of U1)))
qa is Relation-like Function-like set
dom qa is set
rng qa is set
qh is Relation-like ( the Arity of S * ((S,U2,F) #)) . U1 -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like V30(( the Arity of S * ((S,U2,F) #)) . U1,( the ResultSort of S * (S,U2,F)) . U1) Element of bool [:(( the Arity of S * ((S,U2,F) #)) . U1),(( the ResultSort of S * (S,U2,F)) . U1):]
S1 is Relation-like Function-like Element of Args (U1,U2)
(S,U1,U2,F,S1) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
the_arity_of U1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(the_arity_of U1) * (S,U2,F) is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of U1) is countable Element of bool NAT
product ((the_arity_of U1) * (S,U2,F)) is non empty functional with_common_domain product-like set
qh . (S,U1,U2,F,S1) is set
((S,U1,U2,F) * (Den (U1,U2))) . S1 is set
the_arity_of U1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
mc is Relation-like ( the Arity of S * ((S,U2,F) #)) . U1 -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like V30(( the Arity of S * ((S,U2,F) #)) . U1,( the ResultSort of S * (S,U2,F)) . U1) Element of bool [:(( the Arity of S * ((S,U2,F) #)) . U1),(( the ResultSort of S * (S,U2,F)) . U1):]
qa is Relation-like ( the Arity of S * ((S,U2,F) #)) . U1 -defined ( the ResultSort of S * (S,U2,F)) . U1 -valued Function-like V30(( the Arity of S * ((S,U2,F) #)) . U1,( the ResultSort of S * (S,U2,F)) . U1) Element of bool [:(( the Arity of S * ((S,U2,F) #)) . U1),(( the ResultSort of S * (S,U2,F)) . U1):]
dom the Arity of S is Element of bool the carrier' of S
bool the carrier' of S is non empty set
dom ( the Arity of S * ((S,U2,F) #)) is non empty Element of bool the carrier' of S
the Arity of S . U1 is Relation-like NAT -defined Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
((S,U2,F) #) . ( the Arity of S . U1) is non empty set
((S,U2,F) #) . (the_arity_of U1) is non empty set
qh is set
S1 is Relation-like Function-like Element of Args (U1,U2)
(S,U1,U2,F,S1) is Relation-like NAT -defined Function-like (the_arity_of U1) * (S,U2,F) -compatible Element of product ((the_arity_of U1) * (S,U2,F))
(the_arity_of U1) * (S,U2,F) is Relation-like non-empty NAT -defined dom (the_arity_of U1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of U1) is countable Element of bool NAT
product ((the_arity_of U1) * (S,U2,F)) is non empty functional with_common_domain product-like set
mc . qh is set
((S,U1,U2,F) * (Den (U1,U2))) . S1 is set
qa . qh is set
dom mc is Element of bool (( the Arity of S * ((S,U2,F) #)) . U1)
bool (( the Arity of S * ((S,U2,F) #)) . U1) is non empty set
dom qa is Element of bool (( the Arity of S * ((S,U2,F) #)) . U1)
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,U2) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
R is set
mc is Element of the carrier' of S
(S,mc,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . mc -defined ( the ResultSort of S * (S,U1,U2)) . mc -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . mc,( the ResultSort of S * (S,U1,U2)) . mc) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):]
( the Arity of S * ((S,U1,U2) #)) . mc is non empty set
( the ResultSort of S * (S,U1,U2)) . mc is non empty set
[:(( the Arity of S * ((S,U1,U2) #)) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty set
qa is Element of the carrier' of S
(S,qa,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
( the Arity of S * ((S,U1,U2) #)) . qa is non empty set
( the ResultSort of S * (S,U1,U2)) . qa is non empty set
[:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
R is Relation-like Function-like set
dom R is set
mc is non empty Relation-like the carrier' of S -defined Function-like total set
dom mc is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
qa is set
mc . qa is set
qh is Element of the carrier' of S
mc . qh is set
(S,qh,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qh -defined ( the ResultSort of S * (S,U1,U2)) . qh -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qh,( the ResultSort of S * (S,U1,U2)) . qh) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):]
( the Arity of S * ((S,U1,U2) #)) . qh is non empty set
( the ResultSort of S * (S,U1,U2)) . qh is non empty set
[:(( the Arity of S * ((S,U1,U2) #)) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is non empty set
qa is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding set
qh is set
qa . qh is Relation-like Function-like set
( the Arity of S * ((S,U1,U2) #)) . qh is set
( the ResultSort of S * (S,U1,U2)) . qh is set
[:(( the Arity of S * ((S,U1,U2) #)) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . qh),(( the ResultSort of S * (S,U1,U2)) . qh):] is non empty set
S1 is Element of the carrier' of S
qa . S1 is Relation-like Function-like set
(S,S1,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . S1 -defined ( the ResultSort of S * (S,U1,U2)) . S1 -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . S1,( the ResultSort of S * (S,U1,U2)) . S1) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):]
( the Arity of S * ((S,U1,U2) #)) . S1 is non empty set
( the ResultSort of S * (S,U1,U2)) . S1 is non empty set
[:(( the Arity of S * ((S,U1,U2) #)) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty set
qh is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
S1 is Element of the carrier' of S
( the Arity of S * ((S,U1,U2) #)) . S1 is non empty set
( the ResultSort of S * (S,U1,U2)) . S1 is non empty set
qh . S1 is Relation-like ( the Arity of S * ((S,U1,U2) #)) . S1 -defined ( the ResultSort of S * (S,U1,U2)) . S1 -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . S1,( the ResultSort of S * (S,U1,U2)) . S1) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):]
[:(( the Arity of S * ((S,U1,U2) #)) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):] is non empty set
(S,S1,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . S1 -defined ( the ResultSort of S * (S,U1,U2)) . S1 -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . S1,( the ResultSort of S * (S,U1,U2)) . S1) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . S1),(( the ResultSort of S * (S,U1,U2)) . S1):]
F is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
R is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
mc is set
qa is Element of the carrier' of S
( the Arity of S * ((S,U1,U2) #)) . qa is non empty set
( the ResultSort of S * (S,U1,U2)) . qa is non empty set
F . qa is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
[:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
(S,qa,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
F . mc is Relation-like Function-like set
R . mc is Relation-like Function-like set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,U2) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,U2) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,U2),(S,U1,U2) #) is strict MSAlgebra over S
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2) is order-sorted MSAlgebra over S
(S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,U2) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,U2) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,U2),(S,U1,U2) #) is strict MSAlgebra over S
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is Element of the carrier of S
the Sorts of U1 . F is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2,F) is non empty Element of bool (Class (S,U1,U2,(S,F)))
(S,F) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),F) is Element of bool the carrier of S
(S, the Sorts of U1,(S,F)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,F) } is set
(S,U1,U2,(S,F)) is Relation-like (S, the Sorts of U1,(S,F)) -defined (S, the Sorts of U1,(S,F)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):]
[:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,F)),(S, the Sorts of U1,(S,F)):] is non empty set
Class (S,U1,U2,(S,F)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,F))
bool (Class (S,U1,U2,(S,F))) is non empty set
[:( the Sorts of U1 . F),(S,U1,U2,F):] is non empty Relation-like set
bool [:( the Sorts of U1 . F),(S,U1,U2,F):] is non empty set
R is Relation-like the Sorts of U1 . F -defined (S,U1,U2,F) -valued Function-like V30( the Sorts of U1 . F,(S,U1,U2,F)) Element of bool [:( the Sorts of U1 . F),(S,U1,U2,F):]
mc is Relation-like the Sorts of U1 . F -defined (S,U1,U2,F) -valued Function-like V30( the Sorts of U1 . F,(S,U1,U2,F)) Element of bool [:( the Sorts of U1 . F),(S,U1,U2,F):]
qa is set
R . qa is set
qh is Element of the Sorts of U1 . F
(S,U1,U2,F,qh) is Element of (S,U1,U2,F)
Class ((S,U1,U2,(S,F)),qh) is Element of bool (S, the Sorts of U1,(S,F))
bool (S, the Sorts of U1,(S,F)) is non empty set
mc . qa is set
dom R is Element of bool ( the Sorts of U1 . F)
bool ( the Sorts of U1 . F) is non empty set
dom mc is Element of bool ( the Sorts of U1 . F)
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2) is strict non-empty order-sorted MSAlgebra over S
(S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,U2) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,U2) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,U2),(S,U1,U2) #) is strict MSAlgebra over S
the Sorts of (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is Relation-like Function-like set
dom F is set
R is non empty Relation-like the carrier of S -defined Function-like total set
dom R is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
mc is set
R . mc is set
qa is Element of the carrier of S
R . qa is set
(S,U1,U2,qa) is Relation-like the Sorts of U1 . qa -defined (S,U1,U2,qa) -valued Function-like V30( the Sorts of U1 . qa,(S,U1,U2,qa)) Element of bool [:( the Sorts of U1 . qa),(S,U1,U2,qa):]
the Sorts of U1 . qa is non empty set
(S,U1,U2,qa) is non empty Element of bool (Class (S,U1,U2,(S,qa)))
(S,qa) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),qa) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qa)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
(S,U1,U2,(S,qa)) is Relation-like (S, the Sorts of U1,(S,qa)) -defined (S, the Sorts of U1,(S,qa)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):]
[:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is non empty set
Class (S,U1,U2,(S,qa)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qa))
bool (Class (S,U1,U2,(S,qa))) is non empty set
[:( the Sorts of U1 . qa),(S,U1,U2,qa):] is non empty Relation-like set
bool [:( the Sorts of U1 . qa),(S,U1,U2,qa):] is non empty set
mc is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding set
qa is set
mc . qa is Relation-like Function-like set
the Sorts of U1 . qa is set
(S,U1,U2) . qa is set
[:( the Sorts of U1 . qa),((S,U1,U2) . qa):] is Relation-like set
bool [:( the Sorts of U1 . qa),((S,U1,U2) . qa):] is non empty set
qh is Element of the carrier of S
(S,U1,U2,qh) is non empty Element of bool (Class (S,U1,U2,(S,qh)))
(S,qh) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),qh) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qh)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
(S,U1,U2,(S,qh)) is Relation-like (S, the Sorts of U1,(S,qh)) -defined (S, the Sorts of U1,(S,qh)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):]
[:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is non empty set
Class (S,U1,U2,(S,qh)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qh))
bool (Class (S,U1,U2,(S,qh))) is non empty set
mc . qh is Relation-like Function-like set
(S,U1,U2,qh) is Relation-like the Sorts of U1 . qh -defined (S,U1,U2,qh) -valued Function-like V30( the Sorts of U1 . qh,(S,U1,U2,qh)) Element of bool [:( the Sorts of U1 . qh),(S,U1,U2,qh):]
the Sorts of U1 . qh is non empty set
[:( the Sorts of U1 . qh),(S,U1,U2,qh):] is non empty Relation-like set
bool [:( the Sorts of U1 . qh),(S,U1,U2,qh):] is non empty set
qa is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1,(S,U1,U2)
qh is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of (S,U1,U2)
S1 is Element of the carrier of S
the Sorts of U1 . S1 is non empty set
the Sorts of (S,U1,U2) . S1 is non empty set
(S,U1,U2,S1) is non empty Element of bool (Class (S,U1,U2,(S,S1)))
(S,S1) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),S1) is Element of bool the carrier of S
(S, the Sorts of U1,(S,S1)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
(S,U1,U2,(S,S1)) is Relation-like (S, the Sorts of U1,(S,S1)) -defined (S, the Sorts of U1,(S,S1)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,S1)),(S, the Sorts of U1,(S,S1)):]
[:(S, the Sorts of U1,(S,S1)),(S, the Sorts of U1,(S,S1)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,S1)),(S, the Sorts of U1,(S,S1)):] is non empty set
Class (S,U1,U2,(S,S1)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,S1))
bool (Class (S,U1,U2,(S,S1))) is non empty set
qh . S1 is Relation-like the Sorts of U1 . S1 -defined the Sorts of (S,U1,U2) . S1 -valued Function-like V30( the Sorts of U1 . S1, the Sorts of (S,U1,U2) . S1) Element of bool [:( the Sorts of U1 . S1),( the Sorts of (S,U1,U2) . S1):]
[:( the Sorts of U1 . S1),( the Sorts of (S,U1,U2) . S1):] is non empty Relation-like set
bool [:( the Sorts of U1 . S1),( the Sorts of (S,U1,U2) . S1):] is non empty set
(S,U1,U2,S1) is Relation-like the Sorts of U1 . S1 -defined (S,U1,U2,S1) -valued Function-like V30( the Sorts of U1 . S1,(S,U1,U2,S1)) Element of bool [:( the Sorts of U1 . S1),(S,U1,U2,S1):]
[:( the Sorts of U1 . S1),(S,U1,U2,S1):] is non empty Relation-like set
bool [:( the Sorts of U1 . S1),(S,U1,U2,S1):] is non empty set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of (S,U1,U2)
R is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of (S,U1,U2)
mc is set
qa is Element of the carrier of S
the Sorts of U1 . qa is non empty set
the Sorts of (S,U1,U2) . qa is non empty set
(S,U1,U2,qa) is non empty Element of bool (Class (S,U1,U2,(S,qa)))
(S,qa) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),qa) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qa)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qa) } is set
(S,U1,U2,(S,qa)) is Relation-like (S, the Sorts of U1,(S,qa)) -defined (S, the Sorts of U1,(S,qa)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):]
[:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qa)),(S, the Sorts of U1,(S,qa)):] is non empty set
Class (S,U1,U2,(S,qa)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qa))
bool (Class (S,U1,U2,(S,qa))) is non empty set
F . qa is Relation-like the Sorts of U1 . qa -defined the Sorts of (S,U1,U2) . qa -valued Function-like V30( the Sorts of U1 . qa, the Sorts of (S,U1,U2) . qa) Element of bool [:( the Sorts of U1 . qa),( the Sorts of (S,U1,U2) . qa):]
[:( the Sorts of U1 . qa),( the Sorts of (S,U1,U2) . qa):] is non empty Relation-like set
bool [:( the Sorts of U1 . qa),( the Sorts of (S,U1,U2) . qa):] is non empty set
(S,U1,U2,qa) is Relation-like the Sorts of U1 . qa -defined (S,U1,U2,qa) -valued Function-like V30( the Sorts of U1 . qa,(S,U1,U2,qa)) Element of bool [:( the Sorts of U1 . qa),(S,U1,U2,qa):]
[:( the Sorts of U1 . qa),(S,U1,U2,qa):] is non empty Relation-like set
bool [:( the Sorts of U1 . qa),(S,U1,U2,qa):] is non empty set
F . mc is Relation-like Function-like set
R . mc is Relation-like Function-like set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2) is strict non-empty order-sorted MSAlgebra over S
(S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,U2) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,U2) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,U2),(S,U1,U2) #) is strict MSAlgebra over S
(S,U1,U2) is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of (S,U1,U2)
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
qa is Element of the carrier' of S
Args (qa,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
the_result_sort_of qa is Element of the carrier of S
(S,U1,U2) . (the_result_sort_of qa) is Relation-like the Sorts of U1 . (the_result_sort_of qa) -defined the Sorts of (S,U1,U2) . (the_result_sort_of qa) -valued Function-like V30( the Sorts of U1 . (the_result_sort_of qa), the Sorts of (S,U1,U2) . (the_result_sort_of qa)) Element of bool [:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of (S,U1,U2) . (the_result_sort_of qa)):]
the Sorts of U1 . (the_result_sort_of qa) is non empty set
the Sorts of (S,U1,U2) . (the_result_sort_of qa) is non empty set
[:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of (S,U1,U2) . (the_result_sort_of qa)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of (S,U1,U2) . (the_result_sort_of qa)):] is non empty set
Result (qa,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (qa,U1) is Relation-like Args (qa,U1) -defined Result (qa,U1) -valued Function-like V30( Args (qa,U1), Result (qa,U1)) Element of bool [:(Args (qa,U1)),(Result (qa,U1)):]
[:(Args (qa,U1)),(Result (qa,U1)):] is non empty Relation-like set
bool [:(Args (qa,U1)),(Result (qa,U1)):] is non empty set
Args (qa,(S,U1,U2)) is non empty functional Element of rng ( the Sorts of (S,U1,U2) #)
the Sorts of (S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of (S,U1,U2) #) is non empty with_non-empty_elements set
Result (qa,(S,U1,U2)) is non empty Element of rng the Sorts of (S,U1,U2)
rng the Sorts of (S,U1,U2) is non empty with_non-empty_elements set
Den (qa,(S,U1,U2)) is Relation-like Args (qa,(S,U1,U2)) -defined Result (qa,(S,U1,U2)) -valued Function-like V30( Args (qa,(S,U1,U2)), Result (qa,(S,U1,U2))) Element of bool [:(Args (qa,(S,U1,U2))),(Result (qa,(S,U1,U2))):]
[:(Args (qa,(S,U1,U2))),(Result (qa,(S,U1,U2))):] is non empty Relation-like set
bool [:(Args (qa,(S,U1,U2))),(Result (qa,(S,U1,U2))):] is non empty set
qh is Relation-like Function-like Element of Args (qa,U1)
(Den (qa,U1)) . qh is Element of Result (qa,U1)
((S,U1,U2) . (the_result_sort_of qa)) . ((Den (qa,U1)) . qh) is set
(S,U1,U2) # qh is Relation-like Function-like Element of Args (qa,(S,U1,U2))
(Den (qa,(S,U1,U2))) . ((S,U1,U2) # qh) is Element of Result (qa,(S,U1,U2))
the_arity_of qa is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the Arity of S . qa is Relation-like NAT -defined Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
( the Arity of S * ((S,U1,U2) #)) . qa is non empty set
(the_arity_of qa) * (S,U1,U2) is Relation-like non-empty NAT -defined dom (the_arity_of qa) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom (the_arity_of qa) is countable Element of bool NAT
product ((the_arity_of qa) * (S,U1,U2)) is non empty functional with_common_domain product-like set
dom qh is set
(S,qa,U1,U2,qh) is Relation-like NAT -defined Function-like (the_arity_of qa) * (S,U1,U2) -compatible Element of product ((the_arity_of qa) * (S,U1,U2))
sqa is set
((S,U1,U2) # qh) . sqa is set
(S,qa,U1,U2,qh) . sqa is set
s1 is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of qa) /. s1 is Element of the carrier of S
(S,U1,U2,((the_arity_of qa) /. s1)) is Relation-like the Sorts of U1 . ((the_arity_of qa) /. s1) -defined (S,U1,U2,((the_arity_of qa) /. s1)) -valued Function-like V30( the Sorts of U1 . ((the_arity_of qa) /. s1),(S,U1,U2,((the_arity_of qa) /. s1))) Element of bool [:( the Sorts of U1 . ((the_arity_of qa) /. s1)),(S,U1,U2,((the_arity_of qa) /. s1)):]
the Sorts of U1 . ((the_arity_of qa) /. s1) is non empty set
(S,U1,U2,((the_arity_of qa) /. s1)) is non empty Element of bool (Class (S,U1,U2,(S,((the_arity_of qa) /. s1))))
(S,((the_arity_of qa) /. s1)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),((the_arity_of qa) /. s1)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,((the_arity_of qa) /. s1))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of qa) /. s1)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of qa) /. s1)) } is set
(S,U1,U2,(S,((the_arity_of qa) /. s1))) is Relation-like (S, the Sorts of U1,(S,((the_arity_of qa) /. s1))) -defined (S, the Sorts of U1,(S,((the_arity_of qa) /. s1))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,((the_arity_of qa) /. s1))),(S, the Sorts of U1,(S,((the_arity_of qa) /. s1))):]
[:(S, the Sorts of U1,(S,((the_arity_of qa) /. s1))),(S, the Sorts of U1,(S,((the_arity_of qa) /. s1))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,((the_arity_of qa) /. s1))),(S, the Sorts of U1,(S,((the_arity_of qa) /. s1))):] is non empty set
Class (S,U1,U2,(S,((the_arity_of qa) /. s1))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,((the_arity_of qa) /. s1)))
bool (Class (S,U1,U2,(S,((the_arity_of qa) /. s1)))) is non empty set
[:( the Sorts of U1 . ((the_arity_of qa) /. s1)),(S,U1,U2,((the_arity_of qa) /. s1)):] is non empty Relation-like set
bool [:( the Sorts of U1 . ((the_arity_of qa) /. s1)),(S,U1,U2,((the_arity_of qa) /. s1)):] is non empty set
qh . s1 is set
(S,qa,U1,U2,qh) . s1 is set
(the_arity_of qa) * the Sorts of U1 is Relation-like non-empty NAT -defined dom (the_arity_of qa) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
dom ((the_arity_of qa) * the Sorts of U1) is countable Element of bool NAT
((the_arity_of qa) * the Sorts of U1) . s1 is set
(the_arity_of qa) . s1 is set
the Sorts of U1 . ((the_arity_of qa) . s1) is set
(S,U1,U2) . ((the_arity_of qa) /. s1) is Relation-like the Sorts of U1 . ((the_arity_of qa) /. s1) -defined the Sorts of (S,U1,U2) . ((the_arity_of qa) /. s1) -valued Function-like V30( the Sorts of U1 . ((the_arity_of qa) /. s1), the Sorts of (S,U1,U2) . ((the_arity_of qa) /. s1)) Element of bool [:( the Sorts of U1 . ((the_arity_of qa) /. s1)),( the Sorts of (S,U1,U2) . ((the_arity_of qa) /. s1)):]
the Sorts of (S,U1,U2) . ((the_arity_of qa) /. s1) is non empty set
[:( the Sorts of U1 . ((the_arity_of qa) /. s1)),( the Sorts of (S,U1,U2) . ((the_arity_of qa) /. s1)):] is non empty Relation-like set
bool [:( the Sorts of U1 . ((the_arity_of qa) /. s1)),( the Sorts of (S,U1,U2) . ((the_arity_of qa) /. s1)):] is non empty set
((S,U1,U2) . ((the_arity_of qa) /. s1)) . (qh . s1) is set
x is Element of the Sorts of U1 . ((the_arity_of qa) /. s1)
(S,U1,U2,((the_arity_of qa) /. s1)) . x is Element of (S,U1,U2,((the_arity_of qa) /. s1))
x2 is Element of the Sorts of U1 . ((the_arity_of qa) /. s1)
(S,U1,U2,((the_arity_of qa) /. s1),x2) is Element of (S,U1,U2,((the_arity_of qa) /. s1))
Class ((S,U1,U2,(S,((the_arity_of qa) /. s1))),x2) is Element of bool (S, the Sorts of U1,(S,((the_arity_of qa) /. s1)))
bool (S, the Sorts of U1,(S,((the_arity_of qa) /. s1))) is non empty set
dom the Sorts of U1 is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
rng the ResultSort of S is Element of bool the carrier of S
dom the ResultSort of S is Element of bool the carrier' of S
bool the carrier' of S is non empty set
the ResultSort of S * the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
dom ( the ResultSort of S * the Sorts of U1) is non empty Element of bool the carrier' of S
( the ResultSort of S * the Sorts of U1) . qa is non empty set
the ResultSort of S . qa is Element of the carrier of S
the Sorts of U1 . ( the ResultSort of S . qa) is non empty set
rng (Den (qa,U1)) is Element of bool (Result (qa,U1))
bool (Result (qa,U1)) is non empty set
(S,qa,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
( the ResultSort of S * (S,U1,U2)) . qa is non empty set
[:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
dom (S,qa,U1,U2) is Element of bool (( the ResultSort of S * the Sorts of U1) . qa)
bool (( the ResultSort of S * the Sorts of U1) . qa) is non empty set
dom (Den (qa,U1)) is functional Element of bool (Args (qa,U1))
bool (Args (qa,U1)) is non empty set
(S,qa,U1,U2) * (Den (qa,U1)) is Relation-like Args (qa,U1) -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like Element of bool [:(Args (qa,U1)),(( the ResultSort of S * (S,U1,U2)) . qa):]
[:(Args (qa,U1)),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(Args (qa,U1)),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
dom ((S,qa,U1,U2) * (Den (qa,U1))) is functional Element of bool (Args (qa,U1))
dom (S,U1,U2) is non empty Element of bool the carrier of S
dom (S,qa,U1,U2,qh) is countable Element of bool NAT
dom ((the_arity_of qa) * (S,U1,U2)) is countable Element of bool NAT
rng (the_arity_of qa) is Element of bool the carrier of S
dom ((S,U1,U2) # qh) is set
(S,U1,U2) . qa is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
[:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
(S,qa,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
((S,qa,U1,U2) * (Den (qa,U1))) . qh is set
sqa is Element of the Sorts of U1 . (the_result_sort_of qa)
(S,qa,U1,U2) . sqa is set
(S,U1,U2,(the_result_sort_of qa),sqa) is Element of (S,U1,U2,(the_result_sort_of qa))
(S,U1,U2,(the_result_sort_of qa)) is non empty Element of bool (Class (S,U1,U2,(S,(the_result_sort_of qa))))
(S,(the_result_sort_of qa)) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),(the_result_sort_of qa)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,(the_result_sort_of qa))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of qa)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of qa)) } is set
(S,U1,U2,(S,(the_result_sort_of qa))) is Relation-like (S, the Sorts of U1,(S,(the_result_sort_of qa))) -defined (S, the Sorts of U1,(S,(the_result_sort_of qa))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,(the_result_sort_of qa))),(S, the Sorts of U1,(S,(the_result_sort_of qa))):]
[:(S, the Sorts of U1,(S,(the_result_sort_of qa))),(S, the Sorts of U1,(S,(the_result_sort_of qa))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,(the_result_sort_of qa))),(S, the Sorts of U1,(S,(the_result_sort_of qa))):] is non empty set
Class (S,U1,U2,(S,(the_result_sort_of qa))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,(the_result_sort_of qa)))
bool (Class (S,U1,U2,(S,(the_result_sort_of qa)))) is non empty set
Class ((S,U1,U2,(S,(the_result_sort_of qa))),sqa) is Element of bool (S, the Sorts of U1,(S,(the_result_sort_of qa)))
bool (S, the Sorts of U1,(S,(the_result_sort_of qa))) is non empty set
(S,U1,U2,(the_result_sort_of qa)) is Relation-like the Sorts of U1 . (the_result_sort_of qa) -defined (S,U1,U2,(the_result_sort_of qa)) -valued Function-like V30( the Sorts of U1 . (the_result_sort_of qa),(S,U1,U2,(the_result_sort_of qa))) Element of bool [:( the Sorts of U1 . (the_result_sort_of qa)),(S,U1,U2,(the_result_sort_of qa)):]
[:( the Sorts of U1 . (the_result_sort_of qa)),(S,U1,U2,(the_result_sort_of qa)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of qa)),(S,U1,U2,(the_result_sort_of qa)):] is non empty set
(S,U1,U2,(the_result_sort_of qa)) . sqa is Element of (S,U1,U2,(the_result_sort_of qa))
qa is set
(S,U1,U2) . qa is Relation-like Function-like set
rng ((S,U1,U2) . qa) is set
the Sorts of (S,U1,U2) . qa is set
qh is Element of the carrier of S
the Sorts of U1 . qh is non empty set
the Sorts of (S,U1,U2) . qh is non empty set
[:( the Sorts of U1 . qh),( the Sorts of (S,U1,U2) . qh):] is non empty Relation-like set
bool [:( the Sorts of U1 . qh),( the Sorts of (S,U1,U2) . qh):] is non empty set
S1 is Relation-like the Sorts of U1 . qh -defined the Sorts of (S,U1,U2) . qh -valued Function-like V30( the Sorts of U1 . qh, the Sorts of (S,U1,U2) . qh) Element of bool [:( the Sorts of U1 . qh),( the Sorts of (S,U1,U2) . qh):]
dom S1 is Element of bool ( the Sorts of U1 . qh)
bool ( the Sorts of U1 . qh) is non empty set
(S,U1,U2,qh) is non empty Element of bool (Class (S,U1,U2,(S,qh)))
(S,qh) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),qh) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qh)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
(S,U1,U2,(S,qh)) is Relation-like (S, the Sorts of U1,(S,qh)) -defined (S, the Sorts of U1,(S,qh)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):]
[:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is non empty set
Class (S,U1,U2,(S,qh)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qh))
bool (Class (S,U1,U2,(S,qh))) is non empty set
rng S1 is Element of bool ( the Sorts of (S,U1,U2) . qh)
bool ( the Sorts of (S,U1,U2) . qh) is non empty set
S1O is set
(S,U1,U2,qh) is Relation-like the Sorts of U1 . qh -defined (S,U1,U2,qh) -valued Function-like V30( the Sorts of U1 . qh,(S,U1,U2,qh)) Element of bool [:( the Sorts of U1 . qh),(S,U1,U2,qh):]
[:( the Sorts of U1 . qh),(S,U1,U2,qh):] is non empty Relation-like set
bool [:( the Sorts of U1 . qh),(S,U1,U2,qh):] is non empty set
sqa is set
Class ((S,U1,U2,(S,qh)),sqa) is Element of bool (S, the Sorts of U1,(S,qh))
bool (S, the Sorts of U1,(S,qh)) is non empty set
s1 is Element of the Sorts of U1 . qh
(S,U1,U2,qh,s1) is Element of (S,U1,U2,qh)
Class ((S,U1,U2,(S,qh)),s1) is Element of bool (S, the Sorts of U1,(S,qh))
S1 . sqa is set
qh is Element of the carrier of S
S1 is Element of the carrier of S
(S,U1,U2) . qh is Relation-like Function-like set
dom ((S,U1,U2) . qh) is set
(S,U1,U2) . S1 is Relation-like Function-like set
dom ((S,U1,U2) . S1) is set
qa is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
qa . qh is set
qa . S1 is set
S1O is set
((S,U1,U2) . qh) . S1O is set
((S,U1,U2) . S1) . S1O is set
the Sorts of U1 . qh is non empty set
(S,U1,U2) . qh is Relation-like the Sorts of U1 . qh -defined the Sorts of (S,U1,U2) . qh -valued Function-like V30( the Sorts of U1 . qh, the Sorts of (S,U1,U2) . qh) Element of bool [:( the Sorts of U1 . qh),( the Sorts of (S,U1,U2) . qh):]
the Sorts of (S,U1,U2) . qh is non empty set
[:( the Sorts of U1 . qh),( the Sorts of (S,U1,U2) . qh):] is non empty Relation-like set
bool [:( the Sorts of U1 . qh),( the Sorts of (S,U1,U2) . qh):] is non empty set
dom ((S,U1,U2) . qh) is Element of bool ( the Sorts of U1 . qh)
bool ( the Sorts of U1 . qh) is non empty set
the Sorts of U1 . S1 is non empty set
(S,U1,U2) . S1 is Relation-like the Sorts of U1 . S1 -defined the Sorts of (S,U1,U2) . S1 -valued Function-like V30( the Sorts of U1 . S1, the Sorts of (S,U1,U2) . S1) Element of bool [:( the Sorts of U1 . S1),( the Sorts of (S,U1,U2) . S1):]
the Sorts of (S,U1,U2) . S1 is non empty set
[:( the Sorts of U1 . S1),( the Sorts of (S,U1,U2) . S1):] is non empty Relation-like set
bool [:( the Sorts of U1 . S1),( the Sorts of (S,U1,U2) . S1):] is non empty set
dom ((S,U1,U2) . S1) is Element of bool ( the Sorts of U1 . S1)
bool ( the Sorts of U1 . S1) is non empty set
((S,U1,U2) . qh) . S1O is set
(S,U1,U2,qh) is non empty Element of bool (Class (S,U1,U2,(S,qh)))
(S,qh) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),qh) is Element of bool the carrier of S
(S, the Sorts of U1,(S,qh)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,qh) } is set
(S,U1,U2,(S,qh)) is Relation-like (S, the Sorts of U1,(S,qh)) -defined (S, the Sorts of U1,(S,qh)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):]
[:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,qh)),(S, the Sorts of U1,(S,qh)):] is non empty set
Class (S,U1,U2,(S,qh)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,qh))
bool (Class (S,U1,U2,(S,qh))) is non empty set
(S,U1,U2,qh) is Relation-like the Sorts of U1 . qh -defined (S,U1,U2,qh) -valued Function-like V30( the Sorts of U1 . qh,(S,U1,U2,qh)) Element of bool [:( the Sorts of U1 . qh),(S,U1,U2,qh):]
[:( the Sorts of U1 . qh),(S,U1,U2,qh):] is non empty Relation-like set
bool [:( the Sorts of U1 . qh),(S,U1,U2,qh):] is non empty set
s1 is Element of the Sorts of U1 . qh
(S,U1,U2,qh) . s1 is Element of (S,U1,U2,qh)
(S,U1,U2,qh,s1) is Element of (S,U1,U2,qh)
Class ((S,U1,U2,(S,qh)),s1) is Element of bool (S, the Sorts of U1,(S,qh))
bool (S, the Sorts of U1,(S,qh)) is non empty set
sqa is Element of the Sorts of U1 . S1
(S,U1,U2,S1,sqa) is Element of (S,U1,U2,S1)
(S,U1,U2,S1) is non empty Element of bool (Class (S,U1,U2,(S,S1)))
(S,S1) is non empty directed Element of (S)
Class ((S),S1) is Element of bool the carrier of S
(S, the Sorts of U1,(S,S1)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,S1) } is set
(S,U1,U2,(S,S1)) is Relation-like (S, the Sorts of U1,(S,S1)) -defined (S, the Sorts of U1,(S,S1)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,S1)),(S, the Sorts of U1,(S,S1)):]
[:(S, the Sorts of U1,(S,S1)),(S, the Sorts of U1,(S,S1)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,S1)),(S, the Sorts of U1,(S,S1)):] is non empty set
Class (S,U1,U2,(S,S1)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,S1))
bool (Class (S,U1,U2,(S,S1))) is non empty set
Class ((S,U1,U2,(S,S1)),sqa) is Element of bool (S, the Sorts of U1,(S,S1))
bool (S, the Sorts of U1,(S,S1)) is non empty set
(S,U1,U2,S1) is Relation-like the Sorts of U1 . S1 -defined (S,U1,U2,S1) -valued Function-like V30( the Sorts of U1 . S1,(S,U1,U2,S1)) Element of bool [:( the Sorts of U1 . S1),(S,U1,U2,S1):]
[:( the Sorts of U1 . S1),(S,U1,U2,S1):] is non empty Relation-like set
bool [:( the Sorts of U1 . S1),(S,U1,U2,S1):] is non empty set
(S,U1,U2,S1) . sqa is Element of (S,U1,U2,S1)
((S,U1,U2) . S1) . S1O is set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
MSCng F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
mc is Element of the carrier of S
qa is Element of the carrier of S
the Sorts of U1 . mc is non empty set
(MSCng F) . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
[:( the Sorts of U1 . mc),( the Sorts of U1 . mc):] is non empty Relation-like set
bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):] is non empty set
(MSCng F) . qa is Relation-like the Sorts of U1 . qa -defined the Sorts of U1 . qa -valued Element of bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):]
the Sorts of U1 . qa is non empty set
[:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is non empty Relation-like set
bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):] is non empty set
S1O is set
sqa is set
[S1O,sqa] is set
{S1O,sqa} is set
{S1O} is set
{{S1O,sqa},{S1O}} is set
R is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
qh is Element of the carrier of S
R . qh is set
S1 is Element of the carrier of S
R . S1 is set
a1 is Element of the Sorts of U1 . qa
x is Element of the Sorts of U1 . qa
[a1,x] is set
{a1,x} is set
{a1} is set
{{a1,x},{a1}} is set
MSCng (F,qa) is Relation-like the Sorts of U1 . qa -defined the Sorts of U1 . qa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):]
the Sorts of U2 . qa is non empty set
F . qa is Relation-like the Sorts of U1 . qa -defined the Sorts of U2 . qa -valued Function-like V30( the Sorts of U1 . qa, the Sorts of U2 . qa) Element of bool [:( the Sorts of U1 . qa),( the Sorts of U2 . qa):]
[:( the Sorts of U1 . qa),( the Sorts of U2 . qa):] is non empty Relation-like set
bool [:( the Sorts of U1 . qa),( the Sorts of U2 . qa):] is non empty set
(F . qa) . a1 is Element of the Sorts of U2 . qa
(F . qa) . x is Element of the Sorts of U2 . qa
the Sorts of U1 . qh is non empty set
F . qh is Relation-like the Sorts of U1 . qh -defined the Sorts of U2 . qh -valued Function-like V30( the Sorts of U1 . qh, the Sorts of U2 . qh) Element of bool [:( the Sorts of U1 . qh),( the Sorts of U2 . qh):]
the Sorts of U2 . qh is non empty set
[:( the Sorts of U1 . qh),( the Sorts of U2 . qh):] is non empty Relation-like set
bool [:( the Sorts of U1 . qh),( the Sorts of U2 . qh):] is non empty set
dom (F . qh) is Element of bool ( the Sorts of U1 . qh)
bool ( the Sorts of U1 . qh) is non empty set
s1 is Element of the Sorts of U1 . mc
(F . qh) . s1 is set
F . S1 is Relation-like the Sorts of U1 . S1 -defined the Sorts of U2 . S1 -valued Function-like V30( the Sorts of U1 . S1, the Sorts of U2 . S1) Element of bool [:( the Sorts of U1 . S1),( the Sorts of U2 . S1):]
the Sorts of U1 . S1 is non empty set
the Sorts of U2 . S1 is non empty set
[:( the Sorts of U1 . S1),( the Sorts of U2 . S1):] is non empty Relation-like set
bool [:( the Sorts of U1 . S1),( the Sorts of U2 . S1):] is non empty set
(F . S1) . s1 is set
s2 is Element of the Sorts of U1 . mc
(F . qh) . s2 is set
(F . S1) . s2 is set
(MSCng F) . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
MSCng (F,mc) is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
(MSCng F) . qa is Relation-like the Sorts of U1 . qa -defined the Sorts of U1 . qa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . qa),( the Sorts of U1 . qa):]
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
MSCng F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,(S,U1,U2,F)) is strict non-empty order-sorted MSAlgebra over S
(S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,(S,U1,U2,F)) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,(S,U1,U2,F)) #), the ResultSort of S * (S,U1,(S,U1,U2,F))
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,(S,U1,U2,F)) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,(S,U1,U2,F)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,(S,U1,U2,F)),(S,U1,(S,U1,U2,F)) #) is strict MSAlgebra over S
the Sorts of (S,U1,(S,U1,U2,F)) 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 (S,U1,(S,U1,U2,F)) . R is non empty set
the Sorts of U2 . R is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . R),( the Sorts of U2 . R):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . R),( the Sorts of U2 . R):] is non empty set
the Sorts of U1 . R is non empty set
F . R is Relation-like the Sorts of U1 . R -defined the Sorts of U2 . R -valued Function-like V30( the Sorts of U1 . R, the Sorts of U2 . R) Element of bool [:( the Sorts of U1 . R),( the Sorts of U2 . R):]
[:( the Sorts of U1 . R),( the Sorts of U2 . R):] is non empty Relation-like set
bool [:( the Sorts of U1 . R),( the Sorts of U2 . R):] is non empty set
(S,U1,(S,U1,U2,F),R) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,R)))
(S,R) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),R) is Element of bool the carrier of S
(S, the Sorts of U1,(S,R)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
(S,U1,(S,U1,U2,F),(S,R)) is Relation-like (S, the Sorts of U1,(S,R)) -defined (S, the Sorts of U1,(S,R)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):]
[:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,R)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,R))
bool (Class (S,U1,(S,U1,U2,F),(S,R))) is non empty set
S1O is set
sqa is set
Class ((S,U1,(S,U1,U2,F),(S,R)),sqa) is Element of bool (S, the Sorts of U1,(S,R))
bool (S, the Sorts of U1,(S,R)) is non empty set
s1 is Element of the Sorts of U1 . R
(F . R) . s1 is Element of the Sorts of U2 . R
s2 is Element of the Sorts of U2 . R
a1 is Element of the Sorts of U1 . R
(S,U1,(S,U1,U2,F),R,a1) is Element of (S,U1,(S,U1,U2,F),R)
Class ((S,U1,(S,U1,U2,F),(S,R)),a1) is Element of bool (S, the Sorts of U1,(S,R))
(F . R) . a1 is Element of the Sorts of U2 . R
(S,U1,(S,U1,U2,F),R,s1) is Element of (S,U1,(S,U1,U2,F),R)
Class ((S,U1,(S,U1,U2,F),(S,R)),s1) is Element of bool (S, the Sorts of U1,(S,R))
[a1,s1] is set
{a1,s1} is set
{a1} is set
{{a1,s1},{a1}} is set
(S,U1,U2,F) . R is Relation-like the Sorts of U1 . R -defined the Sorts of U1 . R -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):]
[:( the Sorts of U1 . R),( the Sorts of U1 . R):] is non empty Relation-like set
bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):] is non empty set
MSCng F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
(MSCng F) . R is Relation-like the Sorts of U1 . R -defined the Sorts of U1 . R -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):]
MSCng (F,R) is Relation-like the Sorts of U1 . R -defined the Sorts of U1 . R -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):]
S1O is Relation-like Function-like set
dom S1O is set
rng S1O is set
sqa is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . R -defined the Sorts of U2 . R -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . R, the Sorts of U2 . R) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . R),( the Sorts of U2 . R):]
s1 is Element of the Sorts of U1 . R
(S,U1,(S,U1,U2,F),R,s1) is Element of (S,U1,(S,U1,U2,F),R)
Class ((S,U1,(S,U1,U2,F),(S,R)),s1) is Element of bool (S, the Sorts of U1,(S,R))
bool (S, the Sorts of U1,(S,R)) is non empty set
sqa . (S,U1,(S,U1,U2,F),R,s1) is set
(F . R) . s1 is Element of the Sorts of U2 . R
S1O is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . R -defined the Sorts of U2 . R -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . R, the Sorts of U2 . R) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . R),( the Sorts of U2 . R):]
sqa is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . R -defined the Sorts of U2 . R -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . R, the Sorts of U2 . R) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . R),( the Sorts of U2 . R):]
(S,U1,(S,U1,U2,F),R) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,R)))
(S,R) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),R) is Element of bool the carrier of S
(S, the Sorts of U1,(S,R)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,R) } is set
(S,U1,(S,U1,U2,F),(S,R)) is Relation-like (S, the Sorts of U1,(S,R)) -defined (S, the Sorts of U1,(S,R)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):]
[:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,R)),(S, the Sorts of U1,(S,R)):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,R)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,R))
bool (Class (S,U1,(S,U1,U2,F),(S,R))) is non empty set
s1 is set
S1O . s1 is set
sqa . s1 is set
s2 is set
Class ((S,U1,(S,U1,U2,F),(S,R)),s2) is Element of bool (S, the Sorts of U1,(S,R))
bool (S, the Sorts of U1,(S,R)) is non empty set
a1 is Element of the Sorts of U1 . R
(S,U1,(S,U1,U2,F),R,a1) is Element of (S,U1,(S,U1,U2,F),R)
Class ((S,U1,(S,U1,U2,F),(S,R)),a1) is Element of bool (S, the Sorts of U1,(S,R))
(F . R) . a1 is Element of the Sorts of U2 . R
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,(S,U1,U2,F)) is strict non-empty order-sorted MSAlgebra over S
(S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,(S,U1,U2,F)) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,(S,U1,U2,F)) #), the ResultSort of S * (S,U1,(S,U1,U2,F))
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,(S,U1,U2,F)) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,(S,U1,U2,F)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,(S,U1,U2,F)),(S,U1,(S,U1,U2,F)) #) is strict MSAlgebra over S
the Sorts of (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
R is Relation-like Function-like set
dom R is set
mc is non empty Relation-like the carrier of S -defined Function-like total set
dom mc is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
qa is set
mc . qa is set
qh is Element of the carrier of S
mc . qh is set
(S,U1,U2,F,qh) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . qh -defined the Sorts of U2 . qh -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . qh, the Sorts of U2 . qh) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):]
the Sorts of (S,U1,(S,U1,U2,F)) . qh is non empty set
the Sorts of U2 . qh is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):] is non empty set
qa is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding set
qh is set
qa . qh is Relation-like Function-like set
the Sorts of (S,U1,(S,U1,U2,F)) . qh is set
the Sorts of U2 . qh is set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):] is Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):] is non empty set
S1 is Element of the carrier of S
qa . S1 is Relation-like Function-like set
(S,U1,U2,F,S1) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . S1 -defined the Sorts of U2 . S1 -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . S1, the Sorts of U2 . S1) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . S1),( the Sorts of U2 . S1):]
the Sorts of (S,U1,(S,U1,U2,F)) . S1 is non empty set
the Sorts of U2 . S1 is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . S1),( the Sorts of U2 . S1):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . S1),( the Sorts of U2 . S1):] is non empty set
qh is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,(S,U1,U2,F)), the Sorts of U2
S1 is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,(S,U1,U2,F)), the Sorts of U2
S1O is Element of the carrier of S
the Sorts of (S,U1,(S,U1,U2,F)) . S1O is non empty set
the Sorts of U2 . S1O is non empty set
S1 . S1O is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . S1O -defined the Sorts of U2 . S1O -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . S1O, the Sorts of U2 . S1O) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . S1O),( the Sorts of U2 . S1O):]
[:( the Sorts of (S,U1,(S,U1,U2,F)) . S1O),( the Sorts of U2 . S1O):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . S1O),( the Sorts of U2 . S1O):] is non empty set
(S,U1,U2,F,S1O) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . S1O -defined the Sorts of U2 . S1O -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . S1O, the Sorts of U2 . S1O) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . S1O),( the Sorts of U2 . S1O):]
R is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,(S,U1,U2,F)), the Sorts of U2
mc is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,(S,U1,U2,F)), the Sorts of U2
qa is set
qh is Element of the carrier of S
the Sorts of (S,U1,(S,U1,U2,F)) . qh is non empty set
the Sorts of U2 . qh is non empty set
R . qh is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . qh -defined the Sorts of U2 . qh -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . qh, the Sorts of U2 . qh) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):]
[:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):] is non empty set
(S,U1,U2,F,qh) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . qh -defined the Sorts of U2 . qh -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . qh, the Sorts of U2 . qh) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . qh),( the Sorts of U2 . qh):]
R . qa is Relation-like Function-like set
mc . qa is Relation-like Function-like set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,(S,U1,U2,F)) is strict non-empty order-sorted MSAlgebra over S
(S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,(S,U1,U2,F)) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,(S,U1,U2,F)) #), the ResultSort of S * (S,U1,(S,U1,U2,F))
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,(S,U1,U2,F)) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,(S,U1,U2,F)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,(S,U1,U2,F)),(S,U1,(S,U1,U2,F)) #) is strict MSAlgebra over S
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,(S,U1,U2,F)), the Sorts of U2
the Sorts of (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
S1 is Element of the carrier' of S
Args (S1,(S,U1,(S,U1,U2,F))) is non empty functional Element of rng ( the Sorts of (S,U1,(S,U1,U2,F)) #)
the Sorts of (S,U1,(S,U1,U2,F)) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of (S,U1,(S,U1,U2,F)) #) is non empty with_non-empty_elements set
the_result_sort_of S1 is Element of the carrier of S
(S,U1,U2,F) . (the_result_sort_of S1) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1) -defined the Sorts of U2 . (the_result_sort_of S1) -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1), the Sorts of U2 . (the_result_sort_of S1)) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1)),( the Sorts of U2 . (the_result_sort_of S1)):]
the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1) is non empty set
the Sorts of U2 . (the_result_sort_of S1) is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1)),( the Sorts of U2 . (the_result_sort_of S1)):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1)),( the Sorts of U2 . (the_result_sort_of S1)):] is non empty set
Result (S1,(S,U1,(S,U1,U2,F))) is non empty Element of rng the Sorts of (S,U1,(S,U1,U2,F))
rng the Sorts of (S,U1,(S,U1,U2,F)) is non empty with_non-empty_elements set
Den (S1,(S,U1,(S,U1,U2,F))) is Relation-like Args (S1,(S,U1,(S,U1,U2,F))) -defined Result (S1,(S,U1,(S,U1,U2,F))) -valued Function-like V30( Args (S1,(S,U1,(S,U1,U2,F))), Result (S1,(S,U1,(S,U1,U2,F)))) Element of bool [:(Args (S1,(S,U1,(S,U1,U2,F)))),(Result (S1,(S,U1,(S,U1,U2,F)))):]
[:(Args (S1,(S,U1,(S,U1,U2,F)))),(Result (S1,(S,U1,(S,U1,U2,F)))):] is non empty Relation-like set
bool [:(Args (S1,(S,U1,(S,U1,U2,F)))),(Result (S1,(S,U1,(S,U1,U2,F)))):] is non empty set
Args (S1,U2) is non empty functional Element of rng ( the Sorts of U2 #)
the Sorts of U2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U2 #) is non empty with_non-empty_elements set
Result (S1,U2) is non empty Element of rng the Sorts of U2
rng the Sorts of U2 is non empty with_non-empty_elements set
Den (S1,U2) is Relation-like Args (S1,U2) -defined Result (S1,U2) -valued Function-like V30( Args (S1,U2), Result (S1,U2)) Element of bool [:(Args (S1,U2)),(Result (S1,U2)):]
[:(Args (S1,U2)),(Result (S1,U2)):] is non empty Relation-like set
bool [:(Args (S1,U2)),(Result (S1,U2)):] is non empty set
S1O is Relation-like Function-like Element of Args (S1,(S,U1,(S,U1,U2,F)))
(Den (S1,(S,U1,(S,U1,U2,F)))) . S1O is Element of Result (S1,(S,U1,(S,U1,U2,F)))
((S,U1,U2,F) . (the_result_sort_of S1)) . ((Den (S1,(S,U1,(S,U1,U2,F)))) . S1O) is set
(S,U1,U2,F) # S1O is Relation-like Function-like Element of Args (S1,U2)
(Den (S1,U2)) . ((S,U1,U2,F) # S1O) is Element of Result (S1,U2)
the_arity_of S1 is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
dom S1O is set
dom (the_arity_of S1) is countable Element of bool NAT
( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . S1 is non empty set
Args (S1,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
a1 is Relation-like Function-like Element of Args (S1,U1)
(S,S1,U1,(S,U1,U2,F),a1) is Relation-like NAT -defined Function-like (the_arity_of S1) * (S,U1,(S,U1,U2,F)) -compatible Element of product ((the_arity_of S1) * (S,U1,(S,U1,U2,F)))
(the_arity_of S1) * (S,U1,(S,U1,U2,F)) is Relation-like non-empty NAT -defined dom (the_arity_of S1) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
product ((the_arity_of S1) * (S,U1,(S,U1,U2,F))) is non empty functional with_common_domain product-like set
dom a1 is set
x is set
x2 is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of S1) . x2 is set
rng (the_arity_of S1) is Element of bool the carrier of S
bool the carrier of S is non empty set
(the_arity_of S1) /. x2 is Element of the carrier of S
s3 is Element of the carrier of S
the Sorts of U1 . s3 is non empty set
a1 . x2 is set
S1O . x2 is set
s4 is Element of the Sorts of U1 . s3
(S,U1,(S,U1,U2,F),s3,s4) is Element of (S,U1,(S,U1,U2,F),s3)
(S,U1,(S,U1,U2,F),s3) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,s3)))
(S,s3) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),s3) is Element of bool the carrier of S
(S, the Sorts of U1,(S,s3)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s3) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s3) } is set
(S,U1,(S,U1,U2,F),(S,s3)) is Relation-like (S, the Sorts of U1,(S,s3)) -defined (S, the Sorts of U1,(S,s3)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,s3)),(S, the Sorts of U1,(S,s3)):]
[:(S, the Sorts of U1,(S,s3)),(S, the Sorts of U1,(S,s3)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,s3)),(S, the Sorts of U1,(S,s3)):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,s3)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,s3))
bool (Class (S,U1,(S,U1,U2,F),(S,s3))) is non empty set
Class ((S,U1,(S,U1,U2,F),(S,s3)),s4) is Element of bool (S, the Sorts of U1,(S,s3))
bool (S, the Sorts of U1,(S,s3)) is non empty set
((S,U1,U2,F) # S1O) . x2 is set
(S,U1,U2,F) . s3 is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . s3 -defined the Sorts of U2 . s3 -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . s3, the Sorts of U2 . s3) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s3),( the Sorts of U2 . s3):]
the Sorts of (S,U1,(S,U1,U2,F)) . s3 is non empty set
the Sorts of U2 . s3 is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . s3),( the Sorts of U2 . s3):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s3),( the Sorts of U2 . s3):] is non empty set
((S,U1,U2,F) . s3) . (S1O . x2) is set
(S,U1,U2,F,s3) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . s3 -defined the Sorts of U2 . s3 -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . s3, the Sorts of U2 . s3) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s3),( the Sorts of U2 . s3):]
(S,U1,U2,F,s3) . (S,U1,(S,U1,U2,F),s3,s4) is set
F . s3 is Relation-like the Sorts of U1 . s3 -defined the Sorts of U2 . s3 -valued Function-like V30( the Sorts of U1 . s3, the Sorts of U2 . s3) Element of bool [:( the Sorts of U1 . s3),( the Sorts of U2 . s3):]
[:( the Sorts of U1 . s3),( the Sorts of U2 . s3):] is non empty Relation-like set
bool [:( the Sorts of U1 . s3),( the Sorts of U2 . s3):] is non empty set
(F . s3) . s4 is Element of the Sorts of U2 . s3
F # a1 is Relation-like Function-like Element of Args (S1,U2)
(F # a1) . x2 is set
((S,U1,U2,F) # S1O) . x is set
(F # a1) . x is set
the ResultSort of S * the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
dom ( the ResultSort of S * the Sorts of U1) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
( the ResultSort of S * the Sorts of U1) . S1 is non empty set
the ResultSort of S . S1 is Element of the carrier of S
the Sorts of U1 . ( the ResultSort of S . S1) is non empty set
the Sorts of U1 . (the_result_sort_of S1) is non empty set
Result (S1,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (S1,U1) is Relation-like Args (S1,U1) -defined Result (S1,U1) -valued Function-like V30( Args (S1,U1), Result (S1,U1)) Element of bool [:(Args (S1,U1)),(Result (S1,U1)):]
[:(Args (S1,U1)),(Result (S1,U1)):] is non empty Relation-like set
bool [:(Args (S1,U1)),(Result (S1,U1)):] is non empty set
rng (Den (S1,U1)) is Element of bool (Result (S1,U1))
bool (Result (S1,U1)) is non empty set
(S,S1,U1,(S,U1,U2,F)) is Relation-like ( the ResultSort of S * the Sorts of U1) . S1 -defined ( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1 -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . S1,( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1) Element of bool [:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):]
( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1 is non empty set
[:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . S1),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):] is non empty set
dom (S,S1,U1,(S,U1,U2,F)) is Element of bool (( the ResultSort of S * the Sorts of U1) . S1)
bool (( the ResultSort of S * the Sorts of U1) . S1) is non empty set
dom (Den (S1,U1)) is functional Element of bool (Args (S1,U1))
bool (Args (S1,U1)) is non empty set
(S,S1,U1,(S,U1,U2,F)) * (Den (S1,U1)) is Relation-like Args (S1,U1) -defined ( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1 -valued Function-like Element of bool [:(Args (S1,U1)),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):]
[:(Args (S1,U1)),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):] is non empty Relation-like set
bool [:(Args (S1,U1)),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):] is non empty set
dom ((S,S1,U1,(S,U1,U2,F)) * (Den (S1,U1))) is functional Element of bool (Args (S1,U1))
the Arity of S . S1 is Relation-like NAT -defined Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(Den (S1,U1)) . a1 is Element of Result (S1,U1)
(S,U1,U2,F,(the_result_sort_of S1)) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1) -defined the Sorts of U2 . (the_result_sort_of S1) -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1), the Sorts of U2 . (the_result_sort_of S1)) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . (the_result_sort_of S1)),( the Sorts of U2 . (the_result_sort_of S1)):]
(S,U1,(S,U1,U2,F)) . S1 is Relation-like ( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . S1 -defined ( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1 -valued Function-like V30(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . S1,( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1) Element of bool [:(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . S1),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):]
[:(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . S1),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . S1),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . S1):] is non empty set
sqa is Element of the carrier' of S
(S,sqa,U1,(S,U1,U2,F)) is Relation-like ( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . sqa -defined ( the ResultSort of S * (S,U1,(S,U1,U2,F))) . sqa -valued Function-like V30(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . sqa,( the ResultSort of S * (S,U1,(S,U1,U2,F))) . sqa) Element of bool [:(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . sqa),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . sqa):]
( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . sqa is non empty set
( the ResultSort of S * (S,U1,(S,U1,U2,F))) . sqa is non empty set
[:(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . sqa),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . sqa):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,(S,U1,U2,F)) #)) . sqa),(( the ResultSort of S * (S,U1,(S,U1,U2,F))) . sqa):] is non empty set
((S,S1,U1,(S,U1,U2,F)) * (Den (S1,U1))) . a1 is set
x is Element of the Sorts of U1 . (the_result_sort_of S1)
(S,S1,U1,(S,U1,U2,F)) . x is set
(S,U1,(S,U1,U2,F),(the_result_sort_of S1),x) is Element of (S,U1,(S,U1,U2,F),(the_result_sort_of S1))
(S,U1,(S,U1,U2,F),(the_result_sort_of S1)) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,(the_result_sort_of S1))))
(S,(the_result_sort_of S1)) is non empty directed Element of (S)
Class ((S),(the_result_sort_of S1)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,(the_result_sort_of S1))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of S1)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of S1)) } is set
(S,U1,(S,U1,U2,F),(S,(the_result_sort_of S1))) is Relation-like (S, the Sorts of U1,(S,(the_result_sort_of S1))) -defined (S, the Sorts of U1,(S,(the_result_sort_of S1))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,(the_result_sort_of S1))),(S, the Sorts of U1,(S,(the_result_sort_of S1))):]
[:(S, the Sorts of U1,(S,(the_result_sort_of S1))),(S, the Sorts of U1,(S,(the_result_sort_of S1))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,(the_result_sort_of S1))),(S, the Sorts of U1,(S,(the_result_sort_of S1))):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,(the_result_sort_of S1))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,(the_result_sort_of S1)))
bool (Class (S,U1,(S,U1,U2,F),(S,(the_result_sort_of S1)))) is non empty set
Class ((S,U1,(S,U1,U2,F),(S,(the_result_sort_of S1))),x) is Element of bool (S, the Sorts of U1,(S,(the_result_sort_of S1)))
bool (S, the Sorts of U1,(S,(the_result_sort_of S1))) is non empty set
F . (the_result_sort_of S1) is Relation-like the Sorts of U1 . (the_result_sort_of S1) -defined the Sorts of U2 . (the_result_sort_of S1) -valued Function-like V30( the Sorts of U1 . (the_result_sort_of S1), the Sorts of U2 . (the_result_sort_of S1)) Element of bool [:( the Sorts of U1 . (the_result_sort_of S1)),( the Sorts of U2 . (the_result_sort_of S1)):]
[:( the Sorts of U1 . (the_result_sort_of S1)),( the Sorts of U2 . (the_result_sort_of S1)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of S1)),( the Sorts of U2 . (the_result_sort_of S1)):] is non empty set
(F . (the_result_sort_of S1)) . ((Den (S1,U1)) . a1) is set
(Den (S1,U2)) . (F # a1) is Element of Result (S1,U2)
dom ((S,U1,U2,F) # S1O) is set
dom (F # a1) is set
S1 is set
(S,U1,U2,F) . S1 is Relation-like Function-like set
sqa is Element of the carrier of S
(S,U1,U2,F,sqa) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . sqa -defined the Sorts of U2 . sqa -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . sqa, the Sorts of U2 . sqa) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . sqa),( the Sorts of U2 . sqa):]
the Sorts of (S,U1,(S,U1,U2,F)) . sqa is non empty set
the Sorts of U2 . sqa is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . sqa),( the Sorts of U2 . sqa):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . sqa),( the Sorts of U2 . sqa):] is non empty set
dom ((S,U1,U2,F) . S1) is set
s1 is set
s2 is set
((S,U1,U2,F) . S1) . s1 is set
((S,U1,U2,F) . S1) . s2 is set
(S,U1,(S,U1,U2,F)) . sqa is non empty set
(S,U1,(S,U1,U2,F),sqa) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,sqa)))
(S,sqa) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),sqa) is Element of bool the carrier of S
(S, the Sorts of U1,(S,sqa)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,sqa) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,sqa) } is set
(S,U1,(S,U1,U2,F),(S,sqa)) is Relation-like (S, the Sorts of U1,(S,sqa)) -defined (S, the Sorts of U1,(S,sqa)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,sqa)),(S, the Sorts of U1,(S,sqa)):]
[:(S, the Sorts of U1,(S,sqa)),(S, the Sorts of U1,(S,sqa)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,sqa)),(S, the Sorts of U1,(S,sqa)):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,sqa)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,sqa))
bool (Class (S,U1,(S,U1,U2,F),(S,sqa))) is non empty set
the Sorts of U1 . sqa is non empty set
a1 is set
Class ((S,U1,(S,U1,U2,F),(S,sqa)),a1) is Element of bool (S, the Sorts of U1,(S,sqa))
bool (S, the Sorts of U1,(S,sqa)) is non empty set
x is Element of the Sorts of U1 . sqa
(S,U1,(S,U1,U2,F),sqa,x) is Element of (S,U1,(S,U1,U2,F),sqa)
Class ((S,U1,(S,U1,U2,F),(S,sqa)),x) is Element of bool (S, the Sorts of U1,(S,sqa))
x2 is set
Class ((S,U1,(S,U1,U2,F),(S,sqa)),x2) is Element of bool (S, the Sorts of U1,(S,sqa))
F . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U2 . sqa -valued Function-like V30( the Sorts of U1 . sqa, the Sorts of U2 . sqa) Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U2 . sqa):]
[:( the Sorts of U1 . sqa),( the Sorts of U2 . sqa):] is non empty Relation-like set
bool [:( the Sorts of U1 . sqa),( the Sorts of U2 . sqa):] is non empty set
s3 is Element of the Sorts of U1 . sqa
(F . sqa) . s3 is Element of the Sorts of U2 . sqa
(S,U1,(S,U1,U2,F),sqa,s3) is Element of (S,U1,(S,U1,U2,F),sqa)
Class ((S,U1,(S,U1,U2,F),(S,sqa)),s3) is Element of bool (S, the Sorts of U1,(S,sqa))
((S,U1,U2,F) . S1) . (S,U1,(S,U1,U2,F),sqa,s3) is set
(F . sqa) . x is Element of the Sorts of U2 . sqa
((S,U1,U2,F) . S1) . (S,U1,(S,U1,U2,F),sqa,x) is set
[s3,x] is set
{s3,x} is set
{s3} is set
{{s3,x},{s3}} is set
MSCng (F,sqa) is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
[:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty Relation-like set
bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):] is non empty set
MSCng F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
(MSCng F) . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
(S,U1,U2,F) . sqa is Relation-like the Sorts of U1 . sqa -defined the Sorts of U1 . sqa -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . sqa),( the Sorts of U1 . sqa):]
sqa is Element of the carrier of S
s1 is Element of the carrier of S
(S,U1,U2,F) . sqa is Relation-like Function-like set
dom ((S,U1,U2,F) . sqa) is set
(S,U1,U2,F) . s1 is Relation-like Function-like set
dom ((S,U1,U2,F) . s1) is set
s2 is set
((S,U1,U2,F) . sqa) . s2 is set
((S,U1,U2,F) . s1) . s2 is set
the Sorts of (S,U1,(S,U1,U2,F)) . sqa is non empty set
(S,U1,U2,F) . sqa is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . sqa -defined the Sorts of U2 . sqa -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . sqa, the Sorts of U2 . sqa) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . sqa),( the Sorts of U2 . sqa):]
the Sorts of U2 . sqa is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . sqa),( the Sorts of U2 . sqa):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . sqa),( the Sorts of U2 . sqa):] is non empty set
dom ((S,U1,U2,F) . sqa) is Element of bool ( the Sorts of (S,U1,(S,U1,U2,F)) . sqa)
bool ( the Sorts of (S,U1,(S,U1,U2,F)) . sqa) is non empty set
(S,U1,(S,U1,U2,F)) . sqa is non empty set
(S,U1,(S,U1,U2,F),sqa) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,sqa)))
(S,sqa) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),sqa) is Element of bool the carrier of S
(S, the Sorts of U1,(S,sqa)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,sqa) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,sqa) } is set
(S,U1,(S,U1,U2,F),(S,sqa)) is Relation-like (S, the Sorts of U1,(S,sqa)) -defined (S, the Sorts of U1,(S,sqa)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,sqa)),(S, the Sorts of U1,(S,sqa)):]
[:(S, the Sorts of U1,(S,sqa)),(S, the Sorts of U1,(S,sqa)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,sqa)),(S, the Sorts of U1,(S,sqa)):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,sqa)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,sqa))
bool (Class (S,U1,(S,U1,U2,F),(S,sqa))) is non empty set
the Sorts of U1 . sqa is non empty set
a1 is set
Class ((S,U1,(S,U1,U2,F),(S,sqa)),a1) is Element of bool (S, the Sorts of U1,(S,sqa))
bool (S, the Sorts of U1,(S,sqa)) is non empty set
S1 is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
S1 . sqa is set
S1 . s1 is set
the Sorts of U1 . s1 is non empty set
x is Element of the Sorts of U1 . s1
(S,U1,(S,U1,U2,F),s1,x) is Element of (S,U1,(S,U1,U2,F),s1)
(S,U1,(S,U1,U2,F),s1) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,s1)))
(S,s1) is non empty directed Element of (S)
Class ((S),s1) is Element of bool the carrier of S
(S, the Sorts of U1,(S,s1)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s1) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s1) } is set
(S,U1,(S,U1,U2,F),(S,s1)) is Relation-like (S, the Sorts of U1,(S,s1)) -defined (S, the Sorts of U1,(S,s1)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,s1)),(S, the Sorts of U1,(S,s1)):]
[:(S, the Sorts of U1,(S,s1)),(S, the Sorts of U1,(S,s1)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,s1)),(S, the Sorts of U1,(S,s1)):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,s1)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,s1))
bool (Class (S,U1,(S,U1,U2,F),(S,s1))) is non empty set
Class ((S,U1,(S,U1,U2,F),(S,s1)),x) is Element of bool (S, the Sorts of U1,(S,s1))
bool (S, the Sorts of U1,(S,s1)) is non empty set
the Sorts of (S,U1,(S,U1,U2,F)) . s1 is non empty set
(S,U1,U2,F) . s1 is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . s1 -defined the Sorts of U2 . s1 -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . s1, the Sorts of U2 . s1) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s1),( the Sorts of U2 . s1):]
the Sorts of U2 . s1 is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . s1),( the Sorts of U2 . s1):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s1),( the Sorts of U2 . s1):] is non empty set
dom ((S,U1,U2,F) . s1) is Element of bool ( the Sorts of (S,U1,(S,U1,U2,F)) . s1)
bool ( the Sorts of (S,U1,(S,U1,U2,F)) . s1) is non empty set
s4 is Element of the Sorts of U1 . sqa
x2 is Element of the carrier of S
the Sorts of U1 . x2 is non empty set
F . x2 is Relation-like the Sorts of U1 . x2 -defined the Sorts of U2 . x2 -valued Function-like V30( the Sorts of U1 . x2, the Sorts of U2 . x2) Element of bool [:( the Sorts of U1 . x2),( the Sorts of U2 . x2):]
the Sorts of U2 . x2 is non empty set
[:( the Sorts of U1 . x2),( the Sorts of U2 . x2):] is non empty Relation-like set
bool [:( the Sorts of U1 . x2),( the Sorts of U2 . x2):] is non empty set
dom (F . x2) is Element of bool ( the Sorts of U1 . x2)
bool ( the Sorts of U1 . x2) is non empty set
(F . x2) . s4 is set
s3 is Element of the carrier of S
F . s3 is Relation-like the Sorts of U1 . s3 -defined the Sorts of U2 . s3 -valued Function-like V30( the Sorts of U1 . s3, the Sorts of U2 . s3) Element of bool [:( the Sorts of U1 . s3),( the Sorts of U2 . s3):]
the Sorts of U1 . s3 is non empty set
the Sorts of U2 . s3 is non empty set
[:( the Sorts of U1 . s3),( the Sorts of U2 . s3):] is non empty Relation-like set
bool [:( the Sorts of U1 . s3),( the Sorts of U2 . s3):] is non empty set
(F . s3) . s4 is set
S1O is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
S1O . sqa is set
S1O . s1 is set
((S,U1,U2,F) . sqa) . s2 is set
(S,U1,U2,F,sqa) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . sqa -defined the Sorts of U2 . sqa -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . sqa, the Sorts of U2 . sqa) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . sqa),( the Sorts of U2 . sqa):]
(S,U1,(S,U1,U2,F),sqa,s4) is Element of (S,U1,(S,U1,U2,F),sqa)
Class ((S,U1,(S,U1,U2,F),(S,sqa)),s4) is Element of bool (S, the Sorts of U1,(S,sqa))
(S,U1,U2,F,sqa) . (S,U1,(S,U1,U2,F),sqa,s4) is set
F . s1 is Relation-like the Sorts of U1 . s1 -defined the Sorts of U2 . s1 -valued Function-like V30( the Sorts of U1 . s1, the Sorts of U2 . s1) Element of bool [:( the Sorts of U1 . s1),( the Sorts of U2 . s1):]
[:( the Sorts of U1 . s1),( the Sorts of U2 . s1):] is non empty Relation-like set
bool [:( the Sorts of U1 . s1),( the Sorts of U2 . s1):] is non empty set
(F . s1) . s4 is set
(S,U1,U2,F,s1) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . s1 -defined the Sorts of U2 . s1 -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . s1, the Sorts of U2 . s1) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s1),( the Sorts of U2 . s1):]
(S,U1,U2,F,s1) . (S,U1,(S,U1,U2,F),s1,x) is set
((S,U1,U2,F) . s1) . s2 is set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,(S,U1,U2,F)) is strict non-empty order-sorted MSAlgebra over S
(S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,(S,U1,U2,F)) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,(S,U1,U2,F)) #), the ResultSort of S * (S,U1,(S,U1,U2,F))
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,(S,U1,U2,F)) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,(S,U1,U2,F)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,(S,U1,U2,F)),(S,U1,(S,U1,U2,F)) #) is strict MSAlgebra over S
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,(S,U1,U2,F)), the Sorts of U2
the Sorts of (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
sqa is set
(S,U1,U2,F) . sqa is Relation-like Function-like set
rng ((S,U1,U2,F) . sqa) is set
the Sorts of U2 . sqa is set
s2 is Element of the carrier of S
the Sorts of U2 . s2 is non empty set
F . s2 is Relation-like the Sorts of U1 . s2 -defined the Sorts of U2 . s2 -valued Function-like V30( the Sorts of U1 . s2, the Sorts of U2 . s2) Element of bool [:( the Sorts of U1 . s2),( the Sorts of U2 . s2):]
the Sorts of U1 . s2 is non empty set
[:( the Sorts of U1 . s2),( the Sorts of U2 . s2):] is non empty Relation-like set
bool [:( the Sorts of U1 . s2),( the Sorts of U2 . s2):] is non empty set
rng (F . s2) is Element of bool ( the Sorts of U2 . s2)
bool ( the Sorts of U2 . s2) is non empty set
(S,U1,U2,F,s2) is Relation-like the Sorts of (S,U1,(S,U1,U2,F)) . s2 -defined the Sorts of U2 . s2 -valued Function-like V30( the Sorts of (S,U1,(S,U1,U2,F)) . s2, the Sorts of U2 . s2) Element of bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s2),( the Sorts of U2 . s2):]
the Sorts of (S,U1,(S,U1,U2,F)) . s2 is non empty set
[:( the Sorts of (S,U1,(S,U1,U2,F)) . s2),( the Sorts of U2 . s2):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,(S,U1,U2,F)) . s2),( the Sorts of U2 . s2):] is non empty set
dom ((S,U1,U2,F) . sqa) is set
a1 is set
dom (F . s2) is Element of bool ( the Sorts of U1 . s2)
bool ( the Sorts of U1 . s2) is non empty set
x is set
(F . s2) . x is set
(S,U1,(S,U1,U2,F),s2) is non empty Element of bool (Class (S,U1,(S,U1,U2,F),(S,s2)))
(S,s2) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),s2) is Element of bool the carrier of S
(S, the Sorts of U1,(S,s2)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s2) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s2) } is set
(S,U1,(S,U1,U2,F),(S,s2)) is Relation-like (S, the Sorts of U1,(S,s2)) -defined (S, the Sorts of U1,(S,s2)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,s2)),(S, the Sorts of U1,(S,s2)):]
[:(S, the Sorts of U1,(S,s2)),(S, the Sorts of U1,(S,s2)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,s2)),(S, the Sorts of U1,(S,s2)):] is non empty set
Class (S,U1,(S,U1,U2,F),(S,s2)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,s2))
bool (Class (S,U1,(S,U1,U2,F),(S,s2))) is non empty set
x2 is Element of the Sorts of U1 . s2
(S,U1,(S,U1,U2,F),s2,x2) is Element of (S,U1,(S,U1,U2,F),s2)
Class ((S,U1,(S,U1,U2,F),(S,s2)),x2) is Element of bool (S, the Sorts of U1,(S,s2))
bool (S, the Sorts of U1,(S,s2)) is non empty set
((S,U1,U2,F) . sqa) . (S,U1,(S,U1,U2,F),s2,x2) is set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,(S,U1,U2,F)) is strict non-empty order-sorted MSAlgebra over S
(S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,(S,U1,U2,F)) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,(S,U1,U2,F)) #), the ResultSort of S * (S,U1,(S,U1,U2,F))
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,(S,U1,U2,F)) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,(S,U1,U2,F)) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,(S,U1,U2,F)),(S,U1,(S,U1,U2,F)) #) is strict MSAlgebra over S
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,(S,U1,U2,F)), the Sorts of U2
the Sorts of (S,U1,(S,U1,U2,F)) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
[| the Sorts of U1, the Sorts of U1|] is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
R is Element of the carrier of S
mc is Element of the carrier of S
the Sorts of U1 . R is non empty set
U2 . R is Relation-like the Sorts of U1 . R -defined the Sorts of U1 . R -valued Element of bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):]
[:( the Sorts of U1 . R),( the Sorts of U1 . R):] is non empty Relation-like set
bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):] is non empty set
U2 . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
the Sorts of U1 . mc is non empty set
[:( the Sorts of U1 . mc),( the Sorts of U1 . mc):] is non empty Relation-like set
bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):] is non empty set
F is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
qa is Element of the carrier of S
F . qa is set
qh is Element of the carrier of S
F . qh is set
U2 . R is Relation-like the Sorts of U1 . R -defined the Sorts of U1 . R -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . R),( the Sorts of U1 . R):]
U2 . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
S1 is set
S1O is set
[S1,S1O] is set
{S1,S1O} is set
{S1} is set
{{S1,S1O},{S1}} is set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
[| the Sorts of U1, the Sorts of U1|] is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
the carrier' of S is non empty set
R is Element of the carrier' of S
mc is Element of the carrier' of S
Args (R,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
Args (mc,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the_arity_of mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
Result (R,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (R,U1) is Relation-like Args (R,U1) -defined Result (R,U1) -valued Function-like V30( Args (R,U1), Result (R,U1)) Element of bool [:(Args (R,U1)),(Result (R,U1)):]
[:(Args (R,U1)),(Result (R,U1)):] is non empty Relation-like set
bool [:(Args (R,U1)),(Result (R,U1)):] is non empty set
Result (mc,U1) is non empty Element of rng the Sorts of U1
Den (mc,U1) is Relation-like Args (mc,U1) -defined Result (mc,U1) -valued Function-like V30( Args (mc,U1), Result (mc,U1)) Element of bool [:(Args (mc,U1)),(Result (mc,U1)):]
[:(Args (mc,U1)),(Result (mc,U1)):] is non empty Relation-like set
bool [:(Args (mc,U1)),(Result (mc,U1)):] is non empty set
the_result_sort_of mc is Element of the carrier of S
U2 . (the_result_sort_of mc) is Relation-like the Sorts of U1 . (the_result_sort_of mc) -defined the Sorts of U1 . (the_result_sort_of mc) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of mc)),( the Sorts of U1 . (the_result_sort_of mc)):]
the Sorts of U1 . (the_result_sort_of mc) is non empty set
[:( the Sorts of U1 . (the_result_sort_of mc)),( the Sorts of U1 . (the_result_sort_of mc)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of mc)),( the Sorts of U1 . (the_result_sort_of mc)):] is non empty set
the_result_sort_of R is Element of the carrier of S
F is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
F . (the_result_sort_of R) is set
F . (the_result_sort_of mc) is set
S1 is Relation-like Function-like Element of Args (R,U1)
dom S1 is set
(Den (R,U1)) . S1 is Element of Result (R,U1)
S1O is Relation-like Function-like Element of Args (mc,U1)
(Den (mc,U1)) . S1O is Element of Result (mc,U1)
[((Den (R,U1)) . S1),((Den (mc,U1)) . S1O)] is set
{((Den (R,U1)) . S1),((Den (mc,U1)) . S1O)} is set
{((Den (R,U1)) . S1)} is set
{{((Den (R,U1)) . S1),((Den (mc,U1)) . S1O)},{((Den (R,U1)) . S1)}} is set
the Sorts of U1 . (the_result_sort_of R) is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
[| the Sorts of U1, the Sorts of U1|] is non empty Relation-like the carrier of S -defined Function-like total set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
the non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1) (S,U1) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1) (S,U1)
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1) (S,U1)
the carrier' of S is non empty set
F is Element of the carrier' of S
Args (F,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
R is Relation-like Function-like Element of Args (F,U1)
dom R is set
mc is Relation-like Function-like Element of Args (F,U1)
the_arity_of F is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
Result (F,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (F,U1) is Relation-like Args (F,U1) -defined Result (F,U1) -valued Function-like V30( Args (F,U1), Result (F,U1)) Element of bool [:(Args (F,U1)),(Result (F,U1)):]
[:(Args (F,U1)),(Result (F,U1)):] is non empty Relation-like set
bool [:(Args (F,U1)),(Result (F,U1)):] is non empty set
(Den (F,U1)) . R is Element of Result (F,U1)
(Den (F,U1)) . mc is Element of Result (F,U1)
[((Den (F,U1)) . R),((Den (F,U1)) . mc)] is set
{((Den (F,U1)) . R),((Den (F,U1)) . mc)} is set
{((Den (F,U1)) . R)} is set
{{((Den (F,U1)) . R),((Den (F,U1)) . mc)},{((Den (F,U1)) . R)}} is set
the_result_sort_of F is Element of the carrier of S
U2 . (the_result_sort_of F) is Relation-like the Sorts of U1 . (the_result_sort_of F) -defined the Sorts of U1 . (the_result_sort_of F) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of F)),( the Sorts of U1 . (the_result_sort_of F)):]
the Sorts of U1 . (the_result_sort_of F) is non empty set
[:( the Sorts of U1 . (the_result_sort_of F)),( the Sorts of U1 . (the_result_sort_of F)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of F)),( the Sorts of U1 . (the_result_sort_of F)):] is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like (S,U1)
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted monotone MSAlgebra over S
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
the carrier' of S is non empty set
F is Element of the carrier' of S
R is Element of the carrier' of S
Args (F,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
Args (R,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the_arity_of R is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
Result (F,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (F,U1) is Relation-like Args (F,U1) -defined Result (F,U1) -valued Function-like V30( Args (F,U1), Result (F,U1)) Element of bool [:(Args (F,U1)),(Result (F,U1)):]
[:(Args (F,U1)),(Result (F,U1)):] is non empty Relation-like set
bool [:(Args (F,U1)),(Result (F,U1)):] is non empty set
Result (R,U1) is non empty Element of rng the Sorts of U1
Den (R,U1) is Relation-like Args (R,U1) -defined Result (R,U1) -valued Function-like V30( Args (R,U1), Result (R,U1)) Element of bool [:(Args (R,U1)),(Result (R,U1)):]
[:(Args (R,U1)),(Result (R,U1)):] is non empty Relation-like set
bool [:(Args (R,U1)),(Result (R,U1)):] is non empty set
the_result_sort_of R is Element of the carrier of S
U2 . (the_result_sort_of R) is Relation-like the Sorts of U1 . (the_result_sort_of R) -defined the Sorts of U1 . (the_result_sort_of R) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of R)),( the Sorts of U1 . (the_result_sort_of R)):]
the Sorts of U1 . (the_result_sort_of R) is non empty set
[:( the Sorts of U1 . (the_result_sort_of R)),( the Sorts of U1 . (the_result_sort_of R)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of R)),( the Sorts of U1 . (the_result_sort_of R)):] is non empty set
mc is Relation-like Function-like Element of Args (F,U1)
dom mc is set
(Den (F,U1)) . mc is Element of Result (F,U1)
qh is Relation-like Function-like Element of Args (R,U1)
(Den (R,U1)) . qh is Element of Result (R,U1)
[((Den (F,U1)) . mc),((Den (R,U1)) . qh)] is set
{((Den (F,U1)) . mc),((Den (R,U1)) . qh)} is set
{((Den (F,U1)) . mc)} is set
{{((Den (F,U1)) . mc),((Den (R,U1)) . qh)},{((Den (F,U1)) . mc)}} is set
qa is Relation-like Function-like Element of Args (R,U1)
(Den (R,U1)) . qa is Element of Result (R,U1)
[((Den (R,U1)) . qa),((Den (R,U1)) . qh)] is set
{((Den (R,U1)) . qa),((Den (R,U1)) . qh)} is set
{((Den (R,U1)) . qa)} is set
{{((Den (R,U1)) . qa),((Den (R,U1)) . qh)},{((Den (R,U1)) . qa)}} is set
dom (Den (F,U1)) is functional Element of bool (Args (F,U1))
bool (Args (F,U1)) is non empty set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable OverloadedRSSign
U1 is non-empty order-sorted monotone MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
U1 is non-empty order-sorted MSAlgebra over S
the carrier of S is non empty set
U2 is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1) (S,U1)
(S,U1,U2) is strict non-empty order-sorted MSAlgebra over S
(S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,U2) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,U2) #), the ResultSort of S * (S,U1,U2)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,U2) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,U2),(S,U1,U2) #) is strict MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
mc is Element of the carrier' of S
qa is Element of the carrier' of S
Args (qa,(S,U1,U2)) is non empty functional Element of rng ( the Sorts of (S,U1,U2) #)
the Sorts of (S,U1,U2) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
the Sorts of (S,U1,U2) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of (S,U1,U2) #) is non empty with_non-empty_elements set
Result (qa,(S,U1,U2)) is non empty Element of rng the Sorts of (S,U1,U2)
rng the Sorts of (S,U1,U2) is non empty with_non-empty_elements set
Den (qa,(S,U1,U2)) is Relation-like Args (qa,(S,U1,U2)) -defined Result (qa,(S,U1,U2)) -valued Function-like V30( Args (qa,(S,U1,U2)), Result (qa,(S,U1,U2))) Element of bool [:(Args (qa,(S,U1,U2))),(Result (qa,(S,U1,U2))):]
[:(Args (qa,(S,U1,U2))),(Result (qa,(S,U1,U2))):] is non empty Relation-like set
bool [:(Args (qa,(S,U1,U2))),(Result (qa,(S,U1,U2))):] is non empty set
Args (mc,(S,U1,U2)) is non empty functional Element of rng ( the Sorts of (S,U1,U2) #)
(Den (qa,(S,U1,U2))) | (Args (mc,(S,U1,U2))) is Relation-like Args (qa,(S,U1,U2)) -defined Args (mc,(S,U1,U2)) -defined Args (qa,(S,U1,U2)) -defined Result (qa,(S,U1,U2)) -valued Function-like Element of bool [:(Args (qa,(S,U1,U2))),(Result (qa,(S,U1,U2))):]
Den (mc,(S,U1,U2)) is Relation-like Args (mc,(S,U1,U2)) -defined Result (mc,(S,U1,U2)) -valued Function-like V30( Args (mc,(S,U1,U2)), Result (mc,(S,U1,U2))) Element of bool [:(Args (mc,(S,U1,U2))),(Result (mc,(S,U1,U2))):]
Result (mc,(S,U1,U2)) is non empty Element of rng the Sorts of (S,U1,U2)
[:(Args (mc,(S,U1,U2))),(Result (mc,(S,U1,U2))):] is non empty Relation-like set
bool [:(Args (mc,(S,U1,U2))),(Result (mc,(S,U1,U2))):] is non empty set
( the Arity of S * ((S,U1,U2) #)) . qa is non empty set
( the ResultSort of S * (S,U1,U2)) . qa is non empty set
(S,U1,U2) . qa is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
[:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
(S,qa,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
dom the ResultSort of S is Element of bool the carrier' of S
bool the carrier' of S is non empty set
( the Arity of S * ((S,U1,U2) #)) . mc is non empty set
( the ResultSort of S * (S,U1,U2)) . mc is non empty set
(S,U1,U2) . mc is Relation-like ( the Arity of S * ((S,U1,U2) #)) . mc -defined ( the ResultSort of S * (S,U1,U2)) . mc -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . mc,( the ResultSort of S * (S,U1,U2)) . mc) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):]
[:(( the Arity of S * ((S,U1,U2) #)) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,U2) #)) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty set
(S,mc,U1,U2) is Relation-like ( the Arity of S * ((S,U1,U2) #)) . mc -defined ( the ResultSort of S * (S,U1,U2)) . mc -valued Function-like V30(( the Arity of S * ((S,U1,U2) #)) . mc,( the ResultSort of S * (S,U1,U2)) . mc) Element of bool [:(( the Arity of S * ((S,U1,U2) #)) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):]
the_arity_of mc is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
the_arity_of qa is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
len (the_arity_of mc) is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
len (the_arity_of qa) is V4() V5() V6() V10() V11() V12() ext-real V33() Element of NAT
dom (the_arity_of mc) is countable Element of bool NAT
dom (the_arity_of qa) is countable Element of bool NAT
the_result_sort_of mc is Element of the carrier of S
the_result_sort_of qa is Element of the carrier of S
F is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
F . (the_result_sort_of mc) is set
F . (the_result_sort_of qa) is set
dom (Den (mc,(S,U1,U2))) is functional Element of bool (Args (mc,(S,U1,U2)))
bool (Args (mc,(S,U1,U2))) is non empty set
qh is set
(Den (mc,(S,U1,U2))) . qh is set
(Den (qa,(S,U1,U2))) . qh is set
Args (mc,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
S1 is Relation-like Function-like Element of Args (mc,U1)
(S,mc,U1,U2,S1) is Relation-like NAT -defined Function-like (the_arity_of mc) * (S,U1,U2) -compatible Element of product ((the_arity_of mc) * (S,U1,U2))
(the_arity_of mc) * (S,U1,U2) is Relation-like non-empty NAT -defined dom (the_arity_of mc) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
product ((the_arity_of mc) * (S,U1,U2)) is non empty functional with_common_domain product-like set
Result (mc,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
the ResultSort of S * the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
( the ResultSort of S * the Sorts of U1) . mc is non empty set
the ResultSort of S . mc is Element of the carrier of S
the Sorts of U1 . ( the ResultSort of S . mc) is non empty set
the Sorts of U1 . (the_result_sort_of mc) is non empty set
Den (mc,U1) is Relation-like Args (mc,U1) -defined Result (mc,U1) -valued Function-like V30( Args (mc,U1), Result (mc,U1)) Element of bool [:(Args (mc,U1)),(Result (mc,U1)):]
[:(Args (mc,U1)),(Result (mc,U1)):] is non empty Relation-like set
bool [:(Args (mc,U1)),(Result (mc,U1)):] is non empty set
(Den (mc,U1)) . S1 is Element of Result (mc,U1)
the Sorts of U1 . (the_result_sort_of qa) is non empty set
S1O is Element of the Sorts of U1 . (the_result_sort_of mc)
dom (Den (mc,U1)) is functional Element of bool (Args (mc,U1))
bool (Args (mc,U1)) is non empty set
(S,mc,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . mc -defined ( the ResultSort of S * (S,U1,U2)) . mc -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . mc,( the ResultSort of S * (S,U1,U2)) . mc) Element of bool [:(( the ResultSort of S * the Sorts of U1) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):]
[:(( the ResultSort of S * the Sorts of U1) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . mc),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty set
(S,mc,U1,U2) * (Den (mc,U1)) is Relation-like Args (mc,U1) -defined ( the ResultSort of S * (S,U1,U2)) . mc -valued Function-like Element of bool [:(Args (mc,U1)),(( the ResultSort of S * (S,U1,U2)) . mc):]
[:(Args (mc,U1)),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty Relation-like set
bool [:(Args (mc,U1)),(( the ResultSort of S * (S,U1,U2)) . mc):] is non empty set
((S,mc,U1,U2) * (Den (mc,U1))) . S1 is set
(S,mc,U1,U2) . S1O is set
(S,U1,U2,(the_result_sort_of mc),S1O) is Element of (S,U1,U2,(the_result_sort_of mc))
(S,U1,U2,(the_result_sort_of mc)) is non empty Element of bool (Class (S,U1,U2,(S,(the_result_sort_of mc))))
(S,(the_result_sort_of mc)) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),(the_result_sort_of mc)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,(the_result_sort_of mc))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of mc)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of mc)) } is set
(S,U1,U2,(S,(the_result_sort_of mc))) is Relation-like (S, the Sorts of U1,(S,(the_result_sort_of mc))) -defined (S, the Sorts of U1,(S,(the_result_sort_of mc))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,(the_result_sort_of mc))),(S, the Sorts of U1,(S,(the_result_sort_of mc))):]
[:(S, the Sorts of U1,(S,(the_result_sort_of mc))),(S, the Sorts of U1,(S,(the_result_sort_of mc))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,(the_result_sort_of mc))),(S, the Sorts of U1,(S,(the_result_sort_of mc))):] is non empty set
Class (S,U1,U2,(S,(the_result_sort_of mc))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,(the_result_sort_of mc)))
bool (Class (S,U1,U2,(S,(the_result_sort_of mc)))) is non empty set
Class ((S,U1,U2,(S,(the_result_sort_of mc))),S1O) is Element of bool (S, the Sorts of U1,(S,(the_result_sort_of mc)))
bool (S, the Sorts of U1,(S,(the_result_sort_of mc))) is non empty set
(S,mc,U1,U2) . (S,mc,U1,U2,S1) is set
Args (qa,U1) is non empty functional Element of rng ( the Sorts of U1 #)
s1 is Relation-like Function-like Element of Args (qa,U1)
(S,qa,U1,U2,s1) is Relation-like NAT -defined Function-like (the_arity_of qa) * (S,U1,U2) -compatible Element of product ((the_arity_of qa) * (S,U1,U2))
(the_arity_of qa) * (S,U1,U2) is Relation-like non-empty NAT -defined dom (the_arity_of qa) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
product ((the_arity_of qa) * (S,U1,U2)) is non empty functional with_common_domain product-like set
dom S1 is set
s2 is V4() V5() V6() V10() V11() V12() ext-real V33() set
S1 . s2 is set
s1 . s2 is set
[(S1 . s2),(s1 . s2)] is set
{(S1 . s2),(s1 . s2)} is set
{(S1 . s2)} is set
{{(S1 . s2),(s1 . s2)},{(S1 . s2)}} is set
(the_arity_of qa) /. s2 is Element of the carrier of S
U2 . ((the_arity_of qa) /. s2) is Relation-like the Sorts of U1 . ((the_arity_of qa) /. s2) -defined the Sorts of U1 . ((the_arity_of qa) /. s2) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . ((the_arity_of qa) /. s2)),( the Sorts of U1 . ((the_arity_of qa) /. s2)):]
the Sorts of U1 . ((the_arity_of qa) /. s2) is non empty set
[:( the Sorts of U1 . ((the_arity_of qa) /. s2)),( the Sorts of U1 . ((the_arity_of qa) /. s2)):] is non empty Relation-like set
bool [:( the Sorts of U1 . ((the_arity_of qa) /. s2)),( the Sorts of U1 . ((the_arity_of qa) /. s2)):] is non empty set
(the_arity_of mc) /. s2 is Element of the carrier of S
the Sorts of U1 . ((the_arity_of mc) /. s2) is non empty set
(S,mc,U1,U2,S1) . s2 is set
a1 is Element of the Sorts of U1 . ((the_arity_of mc) /. s2)
(S,U1,U2,((the_arity_of mc) /. s2),a1) is Element of (S,U1,U2,((the_arity_of mc) /. s2))
(S,U1,U2,((the_arity_of mc) /. s2)) is non empty Element of bool (Class (S,U1,U2,(S,((the_arity_of mc) /. s2))))
(S,((the_arity_of mc) /. s2)) is non empty directed Element of (S)
Class ((S),((the_arity_of mc) /. s2)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,((the_arity_of mc) /. s2))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of mc) /. s2)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of mc) /. s2)) } is set
(S,U1,U2,(S,((the_arity_of mc) /. s2))) is Relation-like (S, the Sorts of U1,(S,((the_arity_of mc) /. s2))) -defined (S, the Sorts of U1,(S,((the_arity_of mc) /. s2))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,((the_arity_of mc) /. s2))),(S, the Sorts of U1,(S,((the_arity_of mc) /. s2))):]
[:(S, the Sorts of U1,(S,((the_arity_of mc) /. s2))),(S, the Sorts of U1,(S,((the_arity_of mc) /. s2))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,((the_arity_of mc) /. s2))),(S, the Sorts of U1,(S,((the_arity_of mc) /. s2))):] is non empty set
Class (S,U1,U2,(S,((the_arity_of mc) /. s2))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,((the_arity_of mc) /. s2)))
bool (Class (S,U1,U2,(S,((the_arity_of mc) /. s2)))) is non empty set
Class ((S,U1,U2,(S,((the_arity_of mc) /. s2))),a1) is Element of bool (S, the Sorts of U1,(S,((the_arity_of mc) /. s2)))
bool (S, the Sorts of U1,(S,((the_arity_of mc) /. s2))) is non empty set
(the_arity_of mc) . s2 is set
(the_arity_of qa) . s2 is set
x is Element of the carrier of S
x2 is Element of the carrier of S
(S,qa,U1,U2,s1) . s2 is set
s4 is Element of the Sorts of U1 . ((the_arity_of qa) /. s2)
(S,U1,U2,((the_arity_of qa) /. s2),s4) is Element of (S,U1,U2,((the_arity_of qa) /. s2))
(S,U1,U2,((the_arity_of qa) /. s2)) is non empty Element of bool (Class (S,U1,U2,(S,((the_arity_of qa) /. s2))))
(S,((the_arity_of qa) /. s2)) is non empty directed Element of (S)
Class ((S),((the_arity_of qa) /. s2)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,((the_arity_of qa) /. s2))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of qa) /. s2)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,((the_arity_of qa) /. s2)) } is set
(S,U1,U2,(S,((the_arity_of qa) /. s2))) is Relation-like (S, the Sorts of U1,(S,((the_arity_of qa) /. s2))) -defined (S, the Sorts of U1,(S,((the_arity_of qa) /. s2))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,((the_arity_of qa) /. s2))),(S, the Sorts of U1,(S,((the_arity_of qa) /. s2))):]
[:(S, the Sorts of U1,(S,((the_arity_of qa) /. s2))),(S, the Sorts of U1,(S,((the_arity_of qa) /. s2))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,((the_arity_of qa) /. s2))),(S, the Sorts of U1,(S,((the_arity_of qa) /. s2))):] is non empty set
Class (S,U1,U2,(S,((the_arity_of qa) /. s2))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,((the_arity_of qa) /. s2)))
bool (Class (S,U1,U2,(S,((the_arity_of qa) /. s2)))) is non empty set
Class ((S,U1,U2,(S,((the_arity_of qa) /. s2))),s4) is Element of bool (S, the Sorts of U1,(S,((the_arity_of qa) /. s2)))
bool (S, the Sorts of U1,(S,((the_arity_of qa) /. s2))) is non empty set
s3 is Element of the Sorts of U1 . ((the_arity_of qa) /. s2)
(S,U1,U2,((the_arity_of qa) /. s2),s3) is Element of (S,U1,U2,((the_arity_of qa) /. s2))
Class ((S,U1,U2,(S,((the_arity_of qa) /. s2))),s3) is Element of bool (S, the Sorts of U1,(S,((the_arity_of qa) /. s2)))
Result (qa,U1) is non empty Element of rng the Sorts of U1
Den (qa,U1) is Relation-like Args (qa,U1) -defined Result (qa,U1) -valued Function-like V30( Args (qa,U1), Result (qa,U1)) Element of bool [:(Args (qa,U1)),(Result (qa,U1)):]
[:(Args (qa,U1)),(Result (qa,U1)):] is non empty Relation-like set
bool [:(Args (qa,U1)),(Result (qa,U1)):] is non empty set
(Den (qa,U1)) . s1 is Element of Result (qa,U1)
[((Den (mc,U1)) . S1),((Den (qa,U1)) . s1)] is set
{((Den (mc,U1)) . S1),((Den (qa,U1)) . s1)} is set
{((Den (mc,U1)) . S1)} is set
{{((Den (mc,U1)) . S1),((Den (qa,U1)) . s1)},{((Den (mc,U1)) . S1)}} is set
U2 . (the_result_sort_of qa) is Relation-like the Sorts of U1 . (the_result_sort_of qa) -defined the Sorts of U1 . (the_result_sort_of qa) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of U1 . (the_result_sort_of qa)):]
[:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of U1 . (the_result_sort_of qa)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of U1 . (the_result_sort_of qa)):] is non empty set
( the ResultSort of S * the Sorts of U1) . qa is non empty set
the ResultSort of S . qa is Element of the carrier of S
the Sorts of U1 . ( the ResultSort of S . qa) is non empty set
dom (Den (qa,U1)) is functional Element of bool (Args (qa,U1))
bool (Args (qa,U1)) is non empty set
(S,qa,U1,U2) is Relation-like ( the ResultSort of S * the Sorts of U1) . qa -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . qa,( the ResultSort of S * (S,U1,U2)) . qa) Element of bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):]
[:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . qa),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
(S,qa,U1,U2) * (Den (qa,U1)) is Relation-like Args (qa,U1) -defined ( the ResultSort of S * (S,U1,U2)) . qa -valued Function-like Element of bool [:(Args (qa,U1)),(( the ResultSort of S * (S,U1,U2)) . qa):]
[:(Args (qa,U1)),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty Relation-like set
bool [:(Args (qa,U1)),(( the ResultSort of S * (S,U1,U2)) . qa):] is non empty set
((S,qa,U1,U2) * (Den (qa,U1))) . s1 is set
s2 is Element of the Sorts of U1 . (the_result_sort_of qa)
(S,qa,U1,U2) . s2 is set
(S,U1,U2,(the_result_sort_of qa),s2) is Element of (S,U1,U2,(the_result_sort_of qa))
(S,U1,U2,(the_result_sort_of qa)) is non empty Element of bool (Class (S,U1,U2,(S,(the_result_sort_of qa))))
(S,(the_result_sort_of qa)) is non empty directed Element of (S)
Class ((S),(the_result_sort_of qa)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,(the_result_sort_of qa))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of qa)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of qa)) } is set
(S,U1,U2,(S,(the_result_sort_of qa))) is Relation-like (S, the Sorts of U1,(S,(the_result_sort_of qa))) -defined (S, the Sorts of U1,(S,(the_result_sort_of qa))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,(the_result_sort_of qa))),(S, the Sorts of U1,(S,(the_result_sort_of qa))):]
[:(S, the Sorts of U1,(S,(the_result_sort_of qa))),(S, the Sorts of U1,(S,(the_result_sort_of qa))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,(the_result_sort_of qa))),(S, the Sorts of U1,(S,(the_result_sort_of qa))):] is non empty set
Class (S,U1,U2,(S,(the_result_sort_of qa))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,(the_result_sort_of qa)))
bool (Class (S,U1,U2,(S,(the_result_sort_of qa)))) is non empty set
Class ((S,U1,U2,(S,(the_result_sort_of qa))),s2) is Element of bool (S, the Sorts of U1,(S,(the_result_sort_of qa)))
bool (S, the Sorts of U1,(S,(the_result_sort_of qa))) is non empty set
sqa is Element of the Sorts of U1 . (the_result_sort_of qa)
(S,U1,U2,(the_result_sort_of qa),sqa) is Element of (S,U1,U2,(the_result_sort_of qa))
Class ((S,U1,U2,(S,(the_result_sort_of qa))),sqa) is Element of bool (S, the Sorts of U1,(S,(the_result_sort_of qa)))
dom (Den (qa,(S,U1,U2))) is functional Element of bool (Args (qa,(S,U1,U2)))
bool (Args (qa,(S,U1,U2))) is non empty set
(dom (Den (qa,(S,U1,U2)))) /\ (Args (mc,(S,U1,U2))) is functional Element of bool (Args (qa,(S,U1,U2)))
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted monotone MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
the carrier' of S is non empty set
qa is Element of the carrier' of S
qh is Element of the carrier' of S
Args (qa,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
Args (qh,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the_arity_of qh is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
Result (qa,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (qa,U1) is Relation-like Args (qa,U1) -defined Result (qa,U1) -valued Function-like V30( Args (qa,U1), Result (qa,U1)) Element of bool [:(Args (qa,U1)),(Result (qa,U1)):]
[:(Args (qa,U1)),(Result (qa,U1)):] is non empty Relation-like set
bool [:(Args (qa,U1)),(Result (qa,U1)):] is non empty set
Result (qh,U1) is non empty Element of rng the Sorts of U1
Den (qh,U1) is Relation-like Args (qh,U1) -defined Result (qh,U1) -valued Function-like V30( Args (qh,U1), Result (qh,U1)) Element of bool [:(Args (qh,U1)),(Result (qh,U1)):]
[:(Args (qh,U1)),(Result (qh,U1)):] is non empty Relation-like set
bool [:(Args (qh,U1)),(Result (qh,U1)):] is non empty set
the_result_sort_of qh is Element of the carrier of S
(S,U1,U2,F) . (the_result_sort_of qh) is Relation-like the Sorts of U1 . (the_result_sort_of qh) -defined the Sorts of U1 . (the_result_sort_of qh) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U1 . (the_result_sort_of qh)):]
the Sorts of U1 . (the_result_sort_of qh) is non empty set
[:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U1 . (the_result_sort_of qh)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U1 . (the_result_sort_of qh)):] is non empty set
Args (qh,U2) is non empty functional Element of rng ( the Sorts of U2 #)
the Sorts of U2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U2 #) is non empty with_non-empty_elements set
Result (qh,U2) is non empty Element of rng the Sorts of U2
rng the Sorts of U2 is non empty with_non-empty_elements set
Den (qh,U2) is Relation-like Args (qh,U2) -defined Result (qh,U2) -valued Function-like V30( Args (qh,U2), Result (qh,U2)) Element of bool [:(Args (qh,U2)),(Result (qh,U2)):]
[:(Args (qh,U2)),(Result (qh,U2)):] is non empty Relation-like set
bool [:(Args (qh,U2)),(Result (qh,U2)):] is non empty set
Args (qa,U2) is non empty functional Element of rng ( the Sorts of U2 #)
(Den (qh,U2)) | (Args (qa,U2)) is Relation-like Args (qh,U2) -defined Args (qa,U2) -defined Args (qh,U2) -defined Result (qh,U2) -valued Function-like Element of bool [:(Args (qh,U2)),(Result (qh,U2)):]
Den (qa,U2) is Relation-like Args (qa,U2) -defined Result (qa,U2) -valued Function-like V30( Args (qa,U2), Result (qa,U2)) Element of bool [:(Args (qa,U2)),(Result (qa,U2)):]
Result (qa,U2) is non empty Element of rng the Sorts of U2
[:(Args (qa,U2)),(Result (qa,U2)):] is non empty Relation-like set
bool [:(Args (qa,U2)),(Result (qa,U2)):] is non empty set
the_result_sort_of qa is Element of the carrier of S
s1 is Relation-like Function-like Element of Args (qa,U1)
dom s1 is set
(Den (qa,U1)) . s1 is Element of Result (qa,U1)
s2 is Relation-like Function-like Element of Args (qh,U1)
(Den (qh,U1)) . s2 is Element of Result (qh,U1)
[((Den (qa,U1)) . s1),((Den (qh,U1)) . s2)] is set
{((Den (qa,U1)) . s1),((Den (qh,U1)) . s2)} is set
{((Den (qa,U1)) . s1)} is set
{{((Den (qa,U1)) . s1),((Den (qh,U1)) . s2)},{((Den (qa,U1)) . s1)}} is set
MSCng F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
R is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
R . (the_result_sort_of qa) is set
F # s1 is Relation-like Function-like Element of Args (qa,U2)
dom (Den (qa,U2)) is functional Element of bool (Args (qa,U2))
bool (Args (qa,U2)) is non empty set
R . (the_result_sort_of qh) is set
a1 is Relation-like Function-like Element of Args (qh,U1)
(Den (qh,U1)) . a1 is Element of Result (qh,U1)
the Sorts of U1 . (the_result_sort_of qa) is non empty set
F . (the_result_sort_of qa) is Relation-like the Sorts of U1 . (the_result_sort_of qa) -defined the Sorts of U2 . (the_result_sort_of qa) -valued Function-like V30( the Sorts of U1 . (the_result_sort_of qa), the Sorts of U2 . (the_result_sort_of qa)) Element of bool [:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of U2 . (the_result_sort_of qa)):]
the Sorts of U2 . (the_result_sort_of qa) is non empty set
[:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of U2 . (the_result_sort_of qa)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of qa)),( the Sorts of U2 . (the_result_sort_of qa)):] is non empty set
dom (F . (the_result_sort_of qa)) is Element of bool ( the Sorts of U1 . (the_result_sort_of qa))
bool ( the Sorts of U1 . (the_result_sort_of qa)) is non empty set
F . (the_result_sort_of qh) is Relation-like the Sorts of U1 . (the_result_sort_of qh) -defined the Sorts of U2 . (the_result_sort_of qh) -valued Function-like V30( the Sorts of U1 . (the_result_sort_of qh), the Sorts of U2 . (the_result_sort_of qh)) Element of bool [:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U2 . (the_result_sort_of qh)):]
the Sorts of U2 . (the_result_sort_of qh) is non empty set
[:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U2 . (the_result_sort_of qh)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U2 . (the_result_sort_of qh)):] is non empty set
(F . (the_result_sort_of qh)) . ((Den (qa,U1)) . s1) is set
(F . (the_result_sort_of qa)) . ((Den (qa,U1)) . s1) is set
(Den (qa,U2)) . (F # s1) is Element of Result (qa,U2)
(Den (qh,U2)) . (F # s1) is set
F # a1 is Relation-like Function-like Element of Args (qh,U2)
(Den (qh,U2)) . (F # a1) is Element of Result (qh,U2)
(F . (the_result_sort_of qh)) . ((Den (qh,U1)) . a1) is set
s4 is Element of the Sorts of U1 . (the_result_sort_of qh)
x1 is Element of the Sorts of U1 . (the_result_sort_of qh)
[s4,x1] is set
{s4,x1} is set
{s4} is set
{{s4,x1},{s4}} is set
MSCng (F,(the_result_sort_of qh)) is Relation-like the Sorts of U1 . (the_result_sort_of qh) -defined the Sorts of U1 . (the_result_sort_of qh) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U1 . (the_result_sort_of qh)):]
field ((S,U1,U2,F) . (the_result_sort_of qh)) is set
[((Den (qh,U1)) . a1),((Den (qh,U1)) . s2)] is set
{((Den (qh,U1)) . a1),((Den (qh,U1)) . s2)} is set
{((Den (qh,U1)) . a1)} is set
{{((Den (qh,U1)) . a1),((Den (qh,U1)) . s2)},{((Den (qh,U1)) . a1)}} is set
(MSCng F) . (the_result_sort_of qh) is Relation-like the Sorts of U1 . (the_result_sort_of qh) -defined the Sorts of U1 . (the_result_sort_of qh) -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . (the_result_sort_of qh)),( the Sorts of U1 . (the_result_sort_of qh)):]
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
R is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,R) is strict non-empty order-sorted MSAlgebra over S
(S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,R) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,R) #), the ResultSort of S * (S,U1,R)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,R) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,R) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,R),(S,U1,R) #) is strict MSAlgebra over S
the Sorts of (S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
mc is Element of the carrier of S
the Sorts of (S,U1,R) . mc is non empty set
the Sorts of U2 . mc is non empty set
[:( the Sorts of (S,U1,R) . mc),( the Sorts of U2 . mc):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . mc),( the Sorts of U2 . mc):] is non empty set
the Sorts of U1 . mc is non empty set
F . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U2 . mc -valued Function-like V30( the Sorts of U1 . mc, the Sorts of U2 . mc) Element of bool [:( the Sorts of U1 . mc),( the Sorts of U2 . mc):]
[:( the Sorts of U1 . mc),( the Sorts of U2 . mc):] is non empty Relation-like set
bool [:( the Sorts of U1 . mc),( the Sorts of U2 . mc):] is non empty set
(S,U1,R,mc) is non empty Element of bool (Class (S,U1,R,(S,mc)))
(S,mc) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),mc) is Element of bool the carrier of S
(S, the Sorts of U1,(S,mc)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,mc) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,mc) } is set
(S,U1,R,(S,mc)) is Relation-like (S, the Sorts of U1,(S,mc)) -defined (S, the Sorts of U1,(S,mc)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,mc)),(S, the Sorts of U1,(S,mc)):]
[:(S, the Sorts of U1,(S,mc)),(S, the Sorts of U1,(S,mc)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,mc)),(S, the Sorts of U1,(S,mc)):] is non empty set
Class (S,U1,R,(S,mc)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,mc))
bool (Class (S,U1,R,(S,mc))) is non empty set
sqa is set
R . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
[:( the Sorts of U1 . mc),( the Sorts of U1 . mc):] is non empty Relation-like set
bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):] is non empty set
(S,U1,U2,F) . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
s1 is set
Class ((S,U1,R,(S,mc)),s1) is Element of bool (S, the Sorts of U1,(S,mc))
bool (S, the Sorts of U1,(S,mc)) is non empty set
s2 is Element of the Sorts of U1 . mc
(F . mc) . s2 is Element of the Sorts of U2 . mc
a1 is Element of the Sorts of U2 . mc
x is Element of the Sorts of U1 . mc
(S,U1,R,mc,x) is Element of (S,U1,R,mc)
Class ((S,U1,R,(S,mc)),x) is Element of bool (S, the Sorts of U1,(S,mc))
(F . mc) . x is Element of the Sorts of U2 . mc
(S,U1,R,mc,s2) is Element of (S,U1,R,mc)
Class ((S,U1,R,(S,mc)),s2) is Element of bool (S, the Sorts of U1,(S,mc))
[x,s2] is set
{x,s2} is set
{x} is set
{{x,s2},{x}} is set
MSCng F is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like ManySortedRelation of the Sorts of U1, the Sorts of U1
(MSCng F) . mc is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
MSCng (F,mc) is Relation-like the Sorts of U1 . mc -defined the Sorts of U1 . mc -valued total reflexive symmetric transitive Element of bool [:( the Sorts of U1 . mc),( the Sorts of U1 . mc):]
sqa is Relation-like Function-like set
dom sqa is set
rng sqa is set
s1 is Relation-like the Sorts of (S,U1,R) . mc -defined the Sorts of U2 . mc -valued Function-like V30( the Sorts of (S,U1,R) . mc, the Sorts of U2 . mc) Element of bool [:( the Sorts of (S,U1,R) . mc),( the Sorts of U2 . mc):]
s2 is Element of the Sorts of U1 . mc
(S,U1,R,mc,s2) is Element of (S,U1,R,mc)
Class ((S,U1,R,(S,mc)),s2) is Element of bool (S, the Sorts of U1,(S,mc))
bool (S, the Sorts of U1,(S,mc)) is non empty set
s1 . (S,U1,R,mc,s2) is set
(F . mc) . s2 is Element of the Sorts of U2 . mc
sqa is Relation-like the Sorts of (S,U1,R) . mc -defined the Sorts of U2 . mc -valued Function-like V30( the Sorts of (S,U1,R) . mc, the Sorts of U2 . mc) Element of bool [:( the Sorts of (S,U1,R) . mc),( the Sorts of U2 . mc):]
s1 is Relation-like the Sorts of (S,U1,R) . mc -defined the Sorts of U2 . mc -valued Function-like V30( the Sorts of (S,U1,R) . mc, the Sorts of U2 . mc) Element of bool [:( the Sorts of (S,U1,R) . mc),( the Sorts of U2 . mc):]
(S,U1,R,mc) is non empty Element of bool (Class (S,U1,R,(S,mc)))
(S,mc) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),mc) is Element of bool the carrier of S
(S, the Sorts of U1,(S,mc)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,mc) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,mc) } is set
(S,U1,R,(S,mc)) is Relation-like (S, the Sorts of U1,(S,mc)) -defined (S, the Sorts of U1,(S,mc)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,mc)),(S, the Sorts of U1,(S,mc)):]
[:(S, the Sorts of U1,(S,mc)),(S, the Sorts of U1,(S,mc)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,mc)),(S, the Sorts of U1,(S,mc)):] is non empty set
Class (S,U1,R,(S,mc)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,mc))
bool (Class (S,U1,R,(S,mc))) is non empty set
s2 is set
sqa . s2 is set
s1 . s2 is set
a1 is set
Class ((S,U1,R,(S,mc)),a1) is Element of bool (S, the Sorts of U1,(S,mc))
bool (S, the Sorts of U1,(S,mc)) is non empty set
x is Element of the Sorts of U1 . mc
(S,U1,R,mc,x) is Element of (S,U1,R,mc)
Class ((S,U1,R,(S,mc)),x) is Element of bool (S, the Sorts of U1,(S,mc))
(F . mc) . x is Element of the Sorts of U2 . mc
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
R is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,R) is strict non-empty order-sorted MSAlgebra over S
(S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,R) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,R) #), the ResultSort of S * (S,U1,R)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,R) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,R) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,R),(S,U1,R) #) is strict MSAlgebra over S
the Sorts of (S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
mc is Relation-like Function-like set
dom mc is set
qa is non empty Relation-like the carrier of S -defined Function-like total set
dom qa is non empty Element of bool the carrier of S
bool the carrier of S is non empty set
qh is set
qa . qh is set
S1 is Element of the carrier of S
qa . S1 is set
(S,U1,U2,F,R,S1) is Relation-like the Sorts of (S,U1,R) . S1 -defined the Sorts of U2 . S1 -valued Function-like V30( the Sorts of (S,U1,R) . S1, the Sorts of U2 . S1) Element of bool [:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):]
the Sorts of (S,U1,R) . S1 is non empty set
the Sorts of U2 . S1 is non empty set
[:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):] is non empty set
qh is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding set
S1 is set
qh . S1 is Relation-like Function-like set
the Sorts of (S,U1,R) . S1 is set
the Sorts of U2 . S1 is set
[:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):] is Relation-like set
bool [:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):] is non empty set
S1O is Element of the carrier of S
qh . S1O is Relation-like Function-like set
(S,U1,U2,F,R,S1O) is Relation-like the Sorts of (S,U1,R) . S1O -defined the Sorts of U2 . S1O -valued Function-like V30( the Sorts of (S,U1,R) . S1O, the Sorts of U2 . S1O) Element of bool [:( the Sorts of (S,U1,R) . S1O),( the Sorts of U2 . S1O):]
the Sorts of (S,U1,R) . S1O is non empty set
the Sorts of U2 . S1O is non empty set
[:( the Sorts of (S,U1,R) . S1O),( the Sorts of U2 . S1O):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . S1O),( the Sorts of U2 . S1O):] is non empty set
S1 is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,R), the Sorts of U2
S1O is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,R), the Sorts of U2
sqa is Element of the carrier of S
the Sorts of (S,U1,R) . sqa is non empty set
the Sorts of U2 . sqa is non empty set
S1O . sqa is Relation-like the Sorts of (S,U1,R) . sqa -defined the Sorts of U2 . sqa -valued Function-like V30( the Sorts of (S,U1,R) . sqa, the Sorts of U2 . sqa) Element of bool [:( the Sorts of (S,U1,R) . sqa),( the Sorts of U2 . sqa):]
[:( the Sorts of (S,U1,R) . sqa),( the Sorts of U2 . sqa):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . sqa),( the Sorts of U2 . sqa):] is non empty set
(S,U1,U2,F,R,sqa) is Relation-like the Sorts of (S,U1,R) . sqa -defined the Sorts of U2 . sqa -valued Function-like V30( the Sorts of (S,U1,R) . sqa, the Sorts of U2 . sqa) Element of bool [:( the Sorts of (S,U1,R) . sqa),( the Sorts of U2 . sqa):]
mc is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,R), the Sorts of U2
qa is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,R), the Sorts of U2
qh is set
S1 is Element of the carrier of S
the Sorts of (S,U1,R) . S1 is non empty set
the Sorts of U2 . S1 is non empty set
mc . S1 is Relation-like the Sorts of (S,U1,R) . S1 -defined the Sorts of U2 . S1 -valued Function-like V30( the Sorts of (S,U1,R) . S1, the Sorts of U2 . S1) Element of bool [:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):]
[:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):] is non empty set
(S,U1,U2,F,R,S1) is Relation-like the Sorts of (S,U1,R) . S1 -defined the Sorts of U2 . S1 -valued Function-like V30( the Sorts of (S,U1,R) . S1, the Sorts of U2 . S1) Element of bool [:( the Sorts of (S,U1,R) . S1),( the Sorts of U2 . S1):]
mc . qh is Relation-like Function-like set
qa . qh is Relation-like Function-like set
S is non empty non void V73() reflexive transitive antisymmetric order-sorted discernable () OverloadedRSSign
the carrier of S is non empty set
U1 is non-empty order-sorted MSAlgebra over S
the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
U2 is non-empty order-sorted MSAlgebra over S
the Sorts of U2 is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
F is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of U1, the Sorts of U2
(S,U1,U2,F) is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
R is non empty Relation-like the carrier of S -defined Function-like total Relation-yielding MSEquivalence-like MSCongruence-like (S,U1)
(S,U1,R) is strict non-empty order-sorted MSAlgebra over S
(S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total order-sorted set
(S,U1,R) is non empty Relation-like the carrier' of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Arity of S * ((S,U1,R) #), the ResultSort of S * (S,U1,R)
the carrier' of S is non empty set
the Arity of S is Relation-like the carrier' of S -defined the carrier of S * -valued Function-like V30( the carrier' of S, the carrier of S * ) Function-yielding Relation-yielding Element of bool [: the carrier' of S,( the carrier of S *):]
the carrier of S * is non empty functional FinSequence-membered M10( the carrier of S)
[: the carrier' of S,( the carrier of S *):] is non empty Relation-like set
bool [: the carrier' of S,( the carrier of S *):] is non empty set
(S,U1,R) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
the Arity of S * ((S,U1,R) #) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
the ResultSort of S is Relation-like the carrier' of S -defined the carrier of S -valued Function-like V30( the carrier' of S, the carrier of S) Element of bool [: the carrier' of S, the carrier of S:]
[: the carrier' of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier' of S, the carrier of S:] is non empty set
the ResultSort of S * (S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
MSAlgebra(# (S,U1,R),(S,U1,R) #) is strict MSAlgebra over S
(S,U1,U2,F,R) is non empty Relation-like the carrier of S -defined Function-like total Function-yielding Relation-yielding ManySortedFunction of the Sorts of (S,U1,R), the Sorts of U2
the Sorts of (S,U1,R) is non empty Relation-like non-empty non empty-yielding the carrier of S -defined Function-like total set
S1O is Element of the carrier' of S
Args (S1O,(S,U1,R)) is non empty functional Element of rng ( the Sorts of (S,U1,R) #)
the Sorts of (S,U1,R) # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of (S,U1,R) #) is non empty with_non-empty_elements set
the_result_sort_of S1O is Element of the carrier of S
(S,U1,U2,F,R) . (the_result_sort_of S1O) is Relation-like the Sorts of (S,U1,R) . (the_result_sort_of S1O) -defined the Sorts of U2 . (the_result_sort_of S1O) -valued Function-like V30( the Sorts of (S,U1,R) . (the_result_sort_of S1O), the Sorts of U2 . (the_result_sort_of S1O)) Element of bool [:( the Sorts of (S,U1,R) . (the_result_sort_of S1O)),( the Sorts of U2 . (the_result_sort_of S1O)):]
the Sorts of (S,U1,R) . (the_result_sort_of S1O) is non empty set
the Sorts of U2 . (the_result_sort_of S1O) is non empty set
[:( the Sorts of (S,U1,R) . (the_result_sort_of S1O)),( the Sorts of U2 . (the_result_sort_of S1O)):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . (the_result_sort_of S1O)),( the Sorts of U2 . (the_result_sort_of S1O)):] is non empty set
Result (S1O,(S,U1,R)) is non empty Element of rng the Sorts of (S,U1,R)
rng the Sorts of (S,U1,R) is non empty with_non-empty_elements set
Den (S1O,(S,U1,R)) is Relation-like Args (S1O,(S,U1,R)) -defined Result (S1O,(S,U1,R)) -valued Function-like V30( Args (S1O,(S,U1,R)), Result (S1O,(S,U1,R))) Element of bool [:(Args (S1O,(S,U1,R))),(Result (S1O,(S,U1,R))):]
[:(Args (S1O,(S,U1,R))),(Result (S1O,(S,U1,R))):] is non empty Relation-like set
bool [:(Args (S1O,(S,U1,R))),(Result (S1O,(S,U1,R))):] is non empty set
Args (S1O,U2) is non empty functional Element of rng ( the Sorts of U2 #)
the Sorts of U2 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U2 #) is non empty with_non-empty_elements set
Result (S1O,U2) is non empty Element of rng the Sorts of U2
rng the Sorts of U2 is non empty with_non-empty_elements set
Den (S1O,U2) is Relation-like Args (S1O,U2) -defined Result (S1O,U2) -valued Function-like V30( Args (S1O,U2), Result (S1O,U2)) Element of bool [:(Args (S1O,U2)),(Result (S1O,U2)):]
[:(Args (S1O,U2)),(Result (S1O,U2)):] is non empty Relation-like set
bool [:(Args (S1O,U2)),(Result (S1O,U2)):] is non empty set
sqa is Relation-like Function-like Element of Args (S1O,(S,U1,R))
(Den (S1O,(S,U1,R))) . sqa is Element of Result (S1O,(S,U1,R))
((S,U1,U2,F,R) . (the_result_sort_of S1O)) . ((Den (S1O,(S,U1,R))) . sqa) is set
(S,U1,U2,F,R) # sqa is Relation-like Function-like Element of Args (S1O,U2)
(Den (S1O,U2)) . ((S,U1,U2,F,R) # sqa) is Element of Result (S1O,U2)
the_arity_of S1O is Relation-like NAT -defined the carrier of S -valued Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
dom sqa is set
dom (the_arity_of S1O) is countable Element of bool NAT
( the Arity of S * ((S,U1,R) #)) . S1O is non empty set
Args (S1O,U1) is non empty functional Element of rng ( the Sorts of U1 #)
the Sorts of U1 # is non empty Relation-like non-empty non empty-yielding the carrier of S * -defined Function-like total set
rng ( the Sorts of U1 #) is non empty with_non-empty_elements set
x is Relation-like Function-like Element of Args (S1O,U1)
(S,S1O,U1,R,x) is Relation-like NAT -defined Function-like (the_arity_of S1O) * (S,U1,R) -compatible Element of product ((the_arity_of S1O) * (S,U1,R))
(the_arity_of S1O) * (S,U1,R) is Relation-like non-empty NAT -defined dom (the_arity_of S1O) -defined Function-like total V47() FinSequence-like FinSubsequence-like countable set
product ((the_arity_of S1O) * (S,U1,R)) is non empty functional with_common_domain product-like set
dom x is set
x2 is set
s3 is V4() V5() V6() V10() V11() V12() ext-real V33() set
(the_arity_of S1O) . s3 is set
rng (the_arity_of S1O) is Element of bool the carrier of S
bool the carrier of S is non empty set
(the_arity_of S1O) /. s3 is Element of the carrier of S
s4 is Element of the carrier of S
the Sorts of U1 . s4 is non empty set
x . s3 is set
sqa . s3 is set
x1 is Element of the Sorts of U1 . s4
(S,U1,R,s4,x1) is Element of (S,U1,R,s4)
(S,U1,R,s4) is non empty Element of bool (Class (S,U1,R,(S,s4)))
(S,s4) is non empty directed Element of (S)
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),s4) is Element of bool the carrier of S
(S, the Sorts of U1,(S,s4)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s4) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s4) } is set
(S,U1,R,(S,s4)) is Relation-like (S, the Sorts of U1,(S,s4)) -defined (S, the Sorts of U1,(S,s4)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,s4)),(S, the Sorts of U1,(S,s4)):]
[:(S, the Sorts of U1,(S,s4)),(S, the Sorts of U1,(S,s4)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,s4)),(S, the Sorts of U1,(S,s4)):] is non empty set
Class (S,U1,R,(S,s4)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,s4))
bool (Class (S,U1,R,(S,s4))) is non empty set
Class ((S,U1,R,(S,s4)),x1) is Element of bool (S, the Sorts of U1,(S,s4))
bool (S, the Sorts of U1,(S,s4)) is non empty set
((S,U1,U2,F,R) # sqa) . s3 is set
(S,U1,U2,F,R) . s4 is Relation-like the Sorts of (S,U1,R) . s4 -defined the Sorts of U2 . s4 -valued Function-like V30( the Sorts of (S,U1,R) . s4, the Sorts of U2 . s4) Element of bool [:( the Sorts of (S,U1,R) . s4),( the Sorts of U2 . s4):]
the Sorts of (S,U1,R) . s4 is non empty set
the Sorts of U2 . s4 is non empty set
[:( the Sorts of (S,U1,R) . s4),( the Sorts of U2 . s4):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . s4),( the Sorts of U2 . s4):] is non empty set
((S,U1,U2,F,R) . s4) . (sqa . s3) is set
(S,U1,U2,F,R,s4) is Relation-like the Sorts of (S,U1,R) . s4 -defined the Sorts of U2 . s4 -valued Function-like V30( the Sorts of (S,U1,R) . s4, the Sorts of U2 . s4) Element of bool [:( the Sorts of (S,U1,R) . s4),( the Sorts of U2 . s4):]
(S,U1,U2,F,R,s4) . (S,U1,R,s4,x1) is set
F . s4 is Relation-like the Sorts of U1 . s4 -defined the Sorts of U2 . s4 -valued Function-like V30( the Sorts of U1 . s4, the Sorts of U2 . s4) Element of bool [:( the Sorts of U1 . s4),( the Sorts of U2 . s4):]
[:( the Sorts of U1 . s4),( the Sorts of U2 . s4):] is non empty Relation-like set
bool [:( the Sorts of U1 . s4),( the Sorts of U2 . s4):] is non empty set
(F . s4) . x1 is Element of the Sorts of U2 . s4
F # x is Relation-like Function-like Element of Args (S1O,U2)
(F # x) . s3 is set
((S,U1,U2,F,R) # sqa) . x2 is set
(F # x) . x2 is set
the ResultSort of S * the Sorts of U1 is non empty Relation-like non-empty non empty-yielding the carrier' of S -defined Function-like total set
dom ( the ResultSort of S * the Sorts of U1) is non empty Element of bool the carrier' of S
bool the carrier' of S is non empty set
( the ResultSort of S * the Sorts of U1) . S1O is non empty set
the ResultSort of S . S1O is Element of the carrier of S
the Sorts of U1 . ( the ResultSort of S . S1O) is non empty set
the Sorts of U1 . (the_result_sort_of S1O) is non empty set
Result (S1O,U1) is non empty Element of rng the Sorts of U1
rng the Sorts of U1 is non empty with_non-empty_elements set
Den (S1O,U1) is Relation-like Args (S1O,U1) -defined Result (S1O,U1) -valued Function-like V30( Args (S1O,U1), Result (S1O,U1)) Element of bool [:(Args (S1O,U1)),(Result (S1O,U1)):]
[:(Args (S1O,U1)),(Result (S1O,U1)):] is non empty Relation-like set
bool [:(Args (S1O,U1)),(Result (S1O,U1)):] is non empty set
rng (Den (S1O,U1)) is Element of bool (Result (S1O,U1))
bool (Result (S1O,U1)) is non empty set
(S,S1O,U1,R) is Relation-like ( the ResultSort of S * the Sorts of U1) . S1O -defined ( the ResultSort of S * (S,U1,R)) . S1O -valued Function-like V30(( the ResultSort of S * the Sorts of U1) . S1O,( the ResultSort of S * (S,U1,R)) . S1O) Element of bool [:(( the ResultSort of S * the Sorts of U1) . S1O),(( the ResultSort of S * (S,U1,R)) . S1O):]
( the ResultSort of S * (S,U1,R)) . S1O is non empty set
[:(( the ResultSort of S * the Sorts of U1) . S1O),(( the ResultSort of S * (S,U1,R)) . S1O):] is non empty Relation-like set
bool [:(( the ResultSort of S * the Sorts of U1) . S1O),(( the ResultSort of S * (S,U1,R)) . S1O):] is non empty set
dom (S,S1O,U1,R) is Element of bool (( the ResultSort of S * the Sorts of U1) . S1O)
bool (( the ResultSort of S * the Sorts of U1) . S1O) is non empty set
dom (Den (S1O,U1)) is functional Element of bool (Args (S1O,U1))
bool (Args (S1O,U1)) is non empty set
(S,S1O,U1,R) * (Den (S1O,U1)) is Relation-like Args (S1O,U1) -defined ( the ResultSort of S * (S,U1,R)) . S1O -valued Function-like Element of bool [:(Args (S1O,U1)),(( the ResultSort of S * (S,U1,R)) . S1O):]
[:(Args (S1O,U1)),(( the ResultSort of S * (S,U1,R)) . S1O):] is non empty Relation-like set
bool [:(Args (S1O,U1)),(( the ResultSort of S * (S,U1,R)) . S1O):] is non empty set
dom ((S,S1O,U1,R) * (Den (S1O,U1))) is functional Element of bool (Args (S1O,U1))
the Arity of S . S1O is Relation-like NAT -defined Function-like V47() FinSequence-like FinSubsequence-like countable Element of the carrier of S *
(Den (S1O,U1)) . x is Element of Result (S1O,U1)
(S,U1,U2,F,R,(the_result_sort_of S1O)) is Relation-like the Sorts of (S,U1,R) . (the_result_sort_of S1O) -defined the Sorts of U2 . (the_result_sort_of S1O) -valued Function-like V30( the Sorts of (S,U1,R) . (the_result_sort_of S1O), the Sorts of U2 . (the_result_sort_of S1O)) Element of bool [:( the Sorts of (S,U1,R) . (the_result_sort_of S1O)),( the Sorts of U2 . (the_result_sort_of S1O)):]
(S,U1,R) . S1O is Relation-like ( the Arity of S * ((S,U1,R) #)) . S1O -defined ( the ResultSort of S * (S,U1,R)) . S1O -valued Function-like V30(( the Arity of S * ((S,U1,R) #)) . S1O,( the ResultSort of S * (S,U1,R)) . S1O) Element of bool [:(( the Arity of S * ((S,U1,R) #)) . S1O),(( the ResultSort of S * (S,U1,R)) . S1O):]
[:(( the Arity of S * ((S,U1,R) #)) . S1O),(( the ResultSort of S * (S,U1,R)) . S1O):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,R) #)) . S1O),(( the ResultSort of S * (S,U1,R)) . S1O):] is non empty set
s1 is Element of the carrier' of S
(S,s1,U1,R) is Relation-like ( the Arity of S * ((S,U1,R) #)) . s1 -defined ( the ResultSort of S * (S,U1,R)) . s1 -valued Function-like V30(( the Arity of S * ((S,U1,R) #)) . s1,( the ResultSort of S * (S,U1,R)) . s1) Element of bool [:(( the Arity of S * ((S,U1,R) #)) . s1),(( the ResultSort of S * (S,U1,R)) . s1):]
( the Arity of S * ((S,U1,R) #)) . s1 is non empty set
( the ResultSort of S * (S,U1,R)) . s1 is non empty set
[:(( the Arity of S * ((S,U1,R) #)) . s1),(( the ResultSort of S * (S,U1,R)) . s1):] is non empty Relation-like set
bool [:(( the Arity of S * ((S,U1,R) #)) . s1),(( the ResultSort of S * (S,U1,R)) . s1):] is non empty set
((S,S1O,U1,R) * (Den (S1O,U1))) . x is set
x2 is Element of the Sorts of U1 . (the_result_sort_of S1O)
(S,S1O,U1,R) . x2 is set
(S,U1,R,(the_result_sort_of S1O),x2) is Element of (S,U1,R,(the_result_sort_of S1O))
(S,U1,R,(the_result_sort_of S1O)) is non empty Element of bool (Class (S,U1,R,(S,(the_result_sort_of S1O))))
(S,(the_result_sort_of S1O)) is non empty directed Element of (S)
Class ((S),(the_result_sort_of S1O)) is Element of bool the carrier of S
(S, the Sorts of U1,(S,(the_result_sort_of S1O))) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of S1O)) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,(the_result_sort_of S1O)) } is set
(S,U1,R,(S,(the_result_sort_of S1O))) is Relation-like (S, the Sorts of U1,(S,(the_result_sort_of S1O))) -defined (S, the Sorts of U1,(S,(the_result_sort_of S1O))) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,(the_result_sort_of S1O))),(S, the Sorts of U1,(S,(the_result_sort_of S1O))):]
[:(S, the Sorts of U1,(S,(the_result_sort_of S1O))),(S, the Sorts of U1,(S,(the_result_sort_of S1O))):] is Relation-like set
bool [:(S, the Sorts of U1,(S,(the_result_sort_of S1O))),(S, the Sorts of U1,(S,(the_result_sort_of S1O))):] is non empty set
Class (S,U1,R,(S,(the_result_sort_of S1O))) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,(the_result_sort_of S1O)))
bool (Class (S,U1,R,(S,(the_result_sort_of S1O)))) is non empty set
Class ((S,U1,R,(S,(the_result_sort_of S1O))),x2) is Element of bool (S, the Sorts of U1,(S,(the_result_sort_of S1O)))
bool (S, the Sorts of U1,(S,(the_result_sort_of S1O))) is non empty set
F . (the_result_sort_of S1O) is Relation-like the Sorts of U1 . (the_result_sort_of S1O) -defined the Sorts of U2 . (the_result_sort_of S1O) -valued Function-like V30( the Sorts of U1 . (the_result_sort_of S1O), the Sorts of U2 . (the_result_sort_of S1O)) Element of bool [:( the Sorts of U1 . (the_result_sort_of S1O)),( the Sorts of U2 . (the_result_sort_of S1O)):]
[:( the Sorts of U1 . (the_result_sort_of S1O)),( the Sorts of U2 . (the_result_sort_of S1O)):] is non empty Relation-like set
bool [:( the Sorts of U1 . (the_result_sort_of S1O)),( the Sorts of U2 . (the_result_sort_of S1O)):] is non empty set
(F . (the_result_sort_of S1O)) . ((Den (S1O,U1)) . x) is set
(Den (S1O,U2)) . (F # x) is Element of Result (S1O,U2)
dom ((S,U1,U2,F,R) # sqa) is set
dom (F # x) is set
s1 is Element of the carrier of S
s2 is Element of the carrier of S
(S,U1,U2,F,R) . s1 is Relation-like Function-like set
dom ((S,U1,U2,F,R) . s1) is set
(S,U1,U2,F,R) . s2 is Relation-like Function-like set
dom ((S,U1,U2,F,R) . s2) is set
a1 is set
((S,U1,U2,F,R) . s1) . a1 is set
((S,U1,U2,F,R) . s2) . a1 is set
the Sorts of (S,U1,R) . s1 is non empty set
(S,U1,U2,F,R) . s1 is Relation-like the Sorts of (S,U1,R) . s1 -defined the Sorts of U2 . s1 -valued Function-like V30( the Sorts of (S,U1,R) . s1, the Sorts of U2 . s1) Element of bool [:( the Sorts of (S,U1,R) . s1),( the Sorts of U2 . s1):]
the Sorts of U2 . s1 is non empty set
[:( the Sorts of (S,U1,R) . s1),( the Sorts of U2 . s1):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . s1),( the Sorts of U2 . s1):] is non empty set
dom ((S,U1,U2,F,R) . s1) is Element of bool ( the Sorts of (S,U1,R) . s1)
bool ( the Sorts of (S,U1,R) . s1) is non empty set
(S,U1,R) . s1 is non empty set
(S,U1,R,s1) is non empty Element of bool (Class (S,U1,R,(S,s1)))
(S,s1) is non empty directed Element of (S)
bool the carrier of S is non empty set
(S) is non empty Element of bool (bool the carrier of S)
bool (bool the carrier of S) is non empty set
(S) is Relation-like the carrier of S -defined the carrier of S -valued total reflexive symmetric transitive Element of bool [: the carrier of S, the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty Relation-like set
bool [: the carrier of S, the carrier of S:] is non empty set
Class (S) is non empty with_non-empty_elements a_partition of the carrier of S
Class ((S),s1) is Element of bool the carrier of S
(S, the Sorts of U1,(S,s1)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s1) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s1) } is set
(S,U1,R,(S,s1)) is Relation-like (S, the Sorts of U1,(S,s1)) -defined (S, the Sorts of U1,(S,s1)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,s1)),(S, the Sorts of U1,(S,s1)):]
[:(S, the Sorts of U1,(S,s1)),(S, the Sorts of U1,(S,s1)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,s1)),(S, the Sorts of U1,(S,s1)):] is non empty set
Class (S,U1,R,(S,s1)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,s1))
bool (Class (S,U1,R,(S,s1))) is non empty set
the Sorts of U1 . s1 is non empty set
x is set
Class ((S,U1,R,(S,s1)),x) is Element of bool (S, the Sorts of U1,(S,s1))
bool (S, the Sorts of U1,(S,s1)) is non empty set
S1O is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
S1O . s1 is set
S1O . s2 is set
the Sorts of U1 . s2 is non empty set
x2 is Element of the Sorts of U1 . s2
(S,U1,R,s2,x2) is Element of (S,U1,R,s2)
(S,U1,R,s2) is non empty Element of bool (Class (S,U1,R,(S,s2)))
(S,s2) is non empty directed Element of (S)
Class ((S),s2) is Element of bool the carrier of S
(S, the Sorts of U1,(S,s2)) is set
{ ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s2) } is set
union { ( the Sorts of U1 . b₁) where b₁ is Element of the carrier of S : b₁ in (S,s2) } is set
(S,U1,R,(S,s2)) is Relation-like (S, the Sorts of U1,(S,s2)) -defined (S, the Sorts of U1,(S,s2)) -valued total reflexive symmetric transitive Element of bool [:(S, the Sorts of U1,(S,s2)),(S, the Sorts of U1,(S,s2)):]
[:(S, the Sorts of U1,(S,s2)),(S, the Sorts of U1,(S,s2)):] is Relation-like set
bool [:(S, the Sorts of U1,(S,s2)),(S, the Sorts of U1,(S,s2)):] is non empty set
Class (S,U1,R,(S,s2)) is with_non-empty_elements a_partition of (S, the Sorts of U1,(S,s2))
bool (Class (S,U1,R,(S,s2))) is non empty set
Class ((S,U1,R,(S,s2)),x2) is Element of bool (S, the Sorts of U1,(S,s2))
bool (S, the Sorts of U1,(S,s2)) is non empty set
the Sorts of (S,U1,R) . s2 is non empty set
(S,U1,U2,F,R) . s2 is Relation-like the Sorts of (S,U1,R) . s2 -defined the Sorts of U2 . s2 -valued Function-like V30( the Sorts of (S,U1,R) . s2, the Sorts of U2 . s2) Element of bool [:( the Sorts of (S,U1,R) . s2),( the Sorts of U2 . s2):]
the Sorts of U2 . s2 is non empty set
[:( the Sorts of (S,U1,R) . s2),( the Sorts of U2 . s2):] is non empty Relation-like set
bool [:( the Sorts of (S,U1,R) . s2),( the Sorts of U2 . s2):] is non empty set
dom ((S,U1,U2,F,R) . s2) is Element of bool ( the Sorts of (S,U1,R) . s2)
bool ( the Sorts of (S,U1,R) . s2) is non empty set
x1 is Element of the Sorts of U1 . s1
s3 is Element of the carrier of S
the Sorts of U1 . s3 is non empty set
F . s3 is Relation-like the Sorts of U1 . s3 -defined the Sorts of U2 . s3 -valued Function-like V30( the Sorts of U1 . s3, the Sorts of U2 . s3) Element of bool [:( the Sorts of U1 . s3),( the Sorts of U2 . s3):]
the Sorts of U2 . s3 is non empty set
[:( the Sorts of U1 . s3),( the Sorts of U2 . s3):] is non empty Relation-like set
bool [:( the Sorts of U1 . s3),( the Sorts of U2 . s3):] is non empty set
dom (F . s3) is Element of bool ( the Sorts of U1 . s3)
bool ( the Sorts of U1 . s3) is non empty set
(F . s3) . x1 is set
s4 is Element of the carrier of S
F . s4 is Relation-like the Sorts of U1 . s4 -defined the Sorts of U2 . s4 -valued Function-like V30( the Sorts of U1 . s4, the Sorts of U2 . s4) Element of bool [:( the Sorts of U1 . s4),( the Sorts of U2 . s4):]
the Sorts of U1 . s4 is non empty set
the Sorts of U2 . s4 is non empty set
[:( the Sorts of U1 . s4),( the Sorts of U2 . s4):] is non empty Relation-like set
bool [:( the Sorts of U1 . s4),( the Sorts of U2 . s4):] is non empty set
(F . s4) . x1 is set
sqa is non empty Relation-like the carrier of S -defined Function-like total order-sorted set
sqa . s1 is set
sqa . s2 is set
((S,U1,U2,F,R) . s1) . a1 is set
(S,U1,U2,F,R,s1) is Relation-like the Sorts of (S,U1,R) . s1 -defined the Sorts of U2 . s1 -valued Function-like V30( the Sorts of (S,U1,R) . s1, the Sorts of U2 . s1) Element of bool [:( the Sorts of (S,U1,R) . s1),( the Sorts of U2 . s1):]
(S,U1,R,s1,x1) is Element of (S,U1,R,s1)
Class ((S,U1,R,(S,s1)),x1) is Element of bool (S, the Sorts of U1,(S,s1))
(S,U1,U2,F,R,s1) . (S,U1,R,s1,x1) is set
F . s2 is Relation-like the Sorts of U1 . s2 -defined the Sorts of U2 . s2 -valued Function-like V30( the Sorts of U1 . s2, the Sorts of U2 . s2) Element of bool [:( the Sorts of U1 . s2),( the Sorts of U2 . s2):]
[:( the Sorts of U1 . s2),( the Sorts of U2 . s2):] is non empty Relation-like set
bool [:( the Sorts of U1 . s2),( the Sorts of U2 . s2):] is non empty set
(F . s2) . x1 is set
(S,U1,U2,F,R,s2) is Relation-like the Sorts of (S,U1,R) . s2 -defined the Sorts of U2 . s2 -valued Function-like V30( the Sorts of (S,U1,R) . s2, the Sorts of U2 . s2) Element of bool [:( the Sorts of (S,U1,R) . s2),( the Sorts of U2 . s2):]
(S,U1,U2,F,R,s2) . (S,U1,R,s2,x2) is set
((S,U1,U2,F,R) . s2) . a1 is set