:: CATALG_1 semantic presentation

REAL is set
NAT is V6() V7() V8() non empty Element of bool REAL
bool REAL is non empty set
NAT is V6() V7() V8() non empty set
bool NAT is non empty set
bool NAT is non empty set
[:NAT,REAL:] is Relation-like set
bool [:NAT,REAL:] is non empty set
bool (bool REAL) is non empty set
{} is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() set
the Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() set is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() set
1 is V6() V7() V8() V12() non empty Element of NAT
{{},1} is non empty set
K387() is set
bool K387() is non empty set
K388() is Element of bool K387()
K428() is non empty V161() L15()
the carrier of K428() is non empty set
K391( the carrier of K428()) is non empty M36( the carrier of K428())
K427(K428()) is Element of bool K391( the carrier of K428())
bool K391( the carrier of K428()) is non empty set
[:K427(K428()),NAT:] is Relation-like set
bool [:K427(K428()),NAT:] is non empty set
[:NAT,K427(K428()):] is Relation-like set
bool [:NAT,K427(K428()):] is non empty set
2 is V6() V7() V8() V12() non empty Element of NAT
3 is V6() V7() V8() V12() non empty Element of NAT
0 is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() Element of NAT
Seg 1 is non empty V24() V31(1) Element of bool NAT
{1} is non empty set
Seg 2 is non empty V24() V31(2) Element of bool NAT
{1,2} is non empty set
Seg 3 is non empty V24() V31(3) Element of bool NAT
{1,2,3} is non empty set
product {} is set
{{}} is functional non empty set
C1 is set
F is Relation-like Function-like set
C2 is Relation-like Function-like set
S1 is Relation-like C1 -defined Function-like total set
S2 is set
proj1 S1 is set
S1 . S2 is set
dom S1 is Element of bool C1
bool C1 is non empty set
C2 . S2 is set
F | (C2 . S2) is Relation-like Function-like set
S1 is Relation-like C1 -defined Function-like total Function-yielding V78() set
S2 is Relation-like C1 -defined Function-like total Function-yielding V78() set
A1 is set
S1 . A1 is Relation-like Function-like set
C2 . A1 is set
F | (C2 . A1) is Relation-like Function-like set
S2 . A1 is Relation-like Function-like set
C1 is set
C2 is Relation-like C1 -defined Function-like total set
Union C2 is set
id (Union C2) is Relation-like Union C2 -defined Union C2 -valued Function-like one-to-one total V36( Union C2, Union C2) Element of bool [:(Union C2),(Union C2):]
[:(Union C2),(Union C2):] is Relation-like set
bool [:(Union C2),(Union C2):] is non empty set
(C1,C2,(id (Union C2))) is Relation-like C1 -defined Function-like total Function-yielding V78() set
id C2 is Relation-like C1 -defined Function-like total Function-yielding V78() ManySortedFunction of C2,C2
proj2 C2 is set
union (proj2 C2) is set
S2 is set
dom C2 is Element of bool C1
bool C1 is non empty set
C2 . S2 is set
(C1,C2,(id (Union C2))) . S2 is Relation-like Function-like set
(id (Union C2)) | (C2 . S2) is Relation-like Union C2 -defined C2 . S2 -defined Union C2 -defined Union C2 -valued Function-like Element of bool [:(Union C2),(Union C2):]
(id C2) . S2 is Relation-like Function-like set
id (C2 . S2) is Relation-like C2 . S2 -defined C2 . S2 -valued Function-like one-to-one total V36(C2 . S2,C2 . S2) Element of bool [:(C2 . S2),(C2 . S2):]
[:(C2 . S2),(C2 . S2):] is Relation-like set
bool [:(C2 . S2),(C2 . S2):] is non empty set
C1 is set
C2 is Relation-like C1 -defined Function-like total set
F is Relation-like C1 -defined Function-like total set
S1 is Relation-like Function-like set
(C1,C2,S1) is Relation-like C1 -defined Function-like total Function-yielding V78() set
rngs (C1,C2,S1) is Relation-like C1 -defined Function-like total set
S2 is Relation-like Function-like set
S1 * S2 is Relation-like Function-like set
(C1,C2,(S1 * S2)) is Relation-like C1 -defined Function-like total Function-yielding V78() set
(C1,F,S2) is Relation-like C1 -defined Function-like total Function-yielding V78() set
(C1,F,S2) ** (C1,C2,S1) is Relation-like Function-like Function-yielding V78() set
C1 /\ C1 is set
dom (C1,F,S2) is Element of bool C1
bool C1 is non empty set
dom (C1,C2,S1) is Element of bool C1
proj1 ((C1,F,S2) ** (C1,C2,S1)) is set
A1 is set
(C1,C2,S1) . A1 is Relation-like Function-like set
C2 . A1 is set
S1 | (C2 . A1) is Relation-like Function-like set
(rngs (C1,C2,S1)) . A1 is set
proj2 (S1 | (C2 . A1)) is set
F . A1 is set
(S1 * S2) | (C2 . A1) is Relation-like Function-like set
(S1 | (C2 . A1)) * S2 is Relation-like Function-like set
(F . A1) |` (S1 | (C2 . A1)) is Relation-like Function-like set
S2 | (F . A1) is Relation-like Function-like set
(S1 | (C2 . A1)) * (S2 | (F . A1)) is Relation-like Function-like set
(C1,C2,(S1 * S2)) . A1 is Relation-like Function-like set
(C1,F,S2) . A1 is Relation-like Function-like set
((C1,F,S2) ** (C1,C2,S1)) . A1 is Relation-like Function-like set
dom (C1,C2,(S1 * S2)) is Element of bool C1
C1 is Relation-like Function-like set
proj1 C1 is set
C2 is set
F is Relation-like C2 -defined Function-like total set
S1 is Relation-like C2 -defined Function-like total set
(C2,F,C1) is Relation-like C2 -defined Function-like total Function-yielding V78() set
S2 is set
(C2,F,C1) . S2 is Relation-like Function-like set
F . S2 is set
S1 . S2 is set
[:(F . S2),(S1 . S2):] is Relation-like set
bool [:(F . S2),(S1 . S2):] is non empty set
C1 | (F . S2) is Relation-like Function-like set
C1 .: (F . S2) is set
proj2 ((C2,F,C1) . S2) is set
proj1 ((C2,F,C1) . S2) is set
C1 is set
<*C1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
C2 is set
<*C2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
<*C1*> . 1 is set
C1 is non empty feasible feasible ManySortedSign
C1 is non empty feasible feasible ManySortedSign
C2 is MSAlgebra over C1
the Sorts of C2 is Relation-like the carrier of C1 -defined Function-like non empty total set
the carrier of C1 is non empty set
C1 is non empty non void feasible feasible ManySortedSign
the carrier of C1 is non empty set
the Relation-like non-empty non empty-yielding the carrier of C1 -defined Function-like non empty total set is Relation-like non-empty non empty-yielding the carrier of C1 -defined Function-like non empty total set
FreeMSA the Relation-like non-empty non empty-yielding the carrier of C1 -defined Function-like non empty total set is strict non-empty disjoint_valued (C1) MSAlgebra over C1
C1 is non empty non void feasible feasible ManySortedSign
C2 is (C1) MSAlgebra over C1
the Sorts of C2 is Relation-like the carrier of C1 -defined Function-like non empty total set
the carrier of C1 is non empty set
the non empty non void feasible feasible ManySortedSign is non empty non void feasible feasible ManySortedSign
the ( the non empty non void feasible feasible ManySortedSign ) MSAlgebra over the non empty non void feasible feasible ManySortedSign is ( the non empty non void feasible feasible ManySortedSign ) MSAlgebra over the non empty non void feasible feasible ManySortedSign
the Sorts of the ( the non empty non void feasible feasible ManySortedSign ) MSAlgebra over the non empty non void feasible feasible ManySortedSign is Relation-like non empty-yielding the carrier of the non empty non void feasible feasible ManySortedSign -defined Function-like non empty total set
the carrier of the non empty non void feasible feasible ManySortedSign is non empty set
{0} is functional non empty set
C1 is set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
1 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like set
{2} is non empty set
3 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like set
[:{0},(2 -tuples_on C1):] * is functional non empty FinSequence-membered FinSequenceSet of [:{0},(2 -tuples_on C1):]
C2 is set
C2 `2 is set
C1 * is functional non empty FinSequence-membered FinSequenceSet of C1
{ b₁ where b₁ is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 * : len b₁ = 1 } is set
F is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() set
S1 is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 *
len S1 is V6() V7() V8() V12() Element of NAT
S1 . 1 is set
S2 is set
<*S2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*S2*>] is V21() set
{1,<*S2*>} is non empty set
{{1,<*S2*>},{1}} is non empty set
A1 is set
<*S2,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,A1*>] is V21() set
{0,<*S2,A1*>} is functional non empty set
{{0,<*S2,A1*>},{0}} is non empty set
A2 is set
<*S2,A1,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*S2,A1,A2*>] is V21() set
{2,<*S2,A1,A2*>} is non empty set
{{2,<*S2,A1,A2*>},{2}} is non empty set
<*A1,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A1,A2*>] is V21() set
{0,<*A1,A2*>} is functional non empty set
{{0,<*A1,A2*>},{0}} is non empty set
<*[0,<*A1,A2*>],[0,<*S2,A1*>]*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
{S2} is non empty set
rng S1 is Element of bool C1
bool C1 is non empty set
C2 `1 is set
C2 `2 is set
C1 * is functional non empty FinSequence-membered FinSequenceSet of C1
{ b₁ where b₁ is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 * : len b₁ = 3 } is set
F is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 *
len F is V6() V7() V8() V12() Element of NAT
F . 1 is set
F . 2 is set
F . 3 is set
<*(F . 1),(F . 2),(F . 3)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
rng F is Element of bool C1
bool C1 is non empty set
{(F . 1),(F . 2),(F . 3)} is non empty set
<*(F . 2),(F . 3)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . 2),(F . 3)*>] is V21() set
{0,<*(F . 2),(F . 3)*>} is functional non empty set
{{0,<*(F . 2),(F . 3)*>},{0}} is non empty set
<*(F . 1),(F . 2)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . 1),(F . 2)*>] is V21() set
{0,<*(F . 1),(F . 2)*>} is functional non empty set
{{0,<*(F . 1),(F . 2)*>},{0}} is non empty set
<*[0,<*(F . 2),(F . 3)*>],[0,<*(F . 1),(F . 2)*>]*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
f is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
A2 is non empty set
2 -tuples_on A2 is functional non empty FinSequence-membered FinSequenceSet of A2
[:{0},(2 -tuples_on A2):] is Relation-like non empty set
G is Element of [:{0},(2 -tuples_on A2):]
<*G*> is Relation-like NAT -defined [:{0},(2 -tuples_on A2):] -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of [:{0},(2 -tuples_on A2):]
B1 is Element of [:{0},(2 -tuples_on A2):]
<*B1*> is Relation-like NAT -defined [:{0},(2 -tuples_on A2):] -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of [:{0},(2 -tuples_on A2):]
<*G*> ^ <*B1*> is Relation-like NAT -defined [:{0},(2 -tuples_on A2):] -valued Function-like non empty V24() FinSequence-like FinSubsequence-like FinSequence of [:{0},(2 -tuples_on A2):]
<*(F . 1)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*(F . 1)*>] is V21() set
{1,<*(F . 1)*>} is non empty set
{{1,<*(F . 1)*>},{1}} is non empty set
[2,<*(F . 1),(F . 2),(F . 3)*>] is V21() set
{2,<*(F . 1),(F . 2),(F . 3)*>} is non empty set
{{2,<*(F . 1),(F . 2),(F . 3)*>},{2}} is non empty set
C2 `1 is set
C2 is Relation-like Function-like set
proj1 C2 is set
proj2 C2 is set
[:([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):]),([:{0},(2 -tuples_on C1):] *):] is Relation-like set
bool [:([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):]),([:{0},(2 -tuples_on C1):] *):] is non empty set
S1 is set
S1 `2 is set
C1 * is functional non empty FinSequence-membered FinSequenceSet of C1
{ b₁ where b₁ is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 * : len b₁ = 1 } is set
S2 is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 *
len S2 is V6() V7() V8() V12() Element of NAT
S2 . 1 is set
<*(S2 . 1)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
{(S2 . 1)} is non empty set
rng S2 is Element of bool C1
bool C1 is non empty set
<*(S2 . 1),(S2 . 1)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(S2 . 1),(S2 . 1)*>] is V21() set
{0,<*(S2 . 1),(S2 . 1)*>} is functional non empty set
{{0,<*(S2 . 1),(S2 . 1)*>},{0}} is non empty set
G is V21() set
B1 is non empty set
H is Element of B1
<*H,H*> is Relation-like NAT -defined B1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of B1
2 -tuples_on B1 is functional non empty FinSequence-membered FinSequenceSet of B1
<*H*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*H*>] is V21() set
{1,<*H*>} is non empty set
{{1,<*H*>},{1}} is non empty set
<*H,H*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*H,H*>] is V21() set
{0,<*H,H*>} is functional non empty set
{{0,<*H,H*>},{0}} is non empty set
<*H,(S2 . 1),(S2 . 1)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*H,(S2 . 1),(S2 . 1)*>] is V21() set
{2,<*H,(S2 . 1),(S2 . 1)*>} is non empty set
{{2,<*H,(S2 . 1),(S2 . 1)*>},{2}} is non empty set
<*H,(S2 . 1)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*H,(S2 . 1)*>] is V21() set
{0,<*H,(S2 . 1)*>} is functional non empty set
{{0,<*H,(S2 . 1)*>},{0}} is non empty set
S1 `1 is set
<*H*> is Relation-like NAT -defined B1 -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of B1
[1,<*H*>] is V21() set
{1,<*H*>} is non empty set
{{1,<*H*>},{1}} is non empty set
[0,<*H,H*>] is V21() set
{0,<*H,H*>} is functional non empty set
{{0,<*H,H*>},{0}} is non empty set
S1 `2 is set
C1 * is functional non empty FinSequence-membered FinSequenceSet of C1
{ b₁ where b₁ is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 * : len b₁ = 3 } is set
S2 is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 *
len S2 is V6() V7() V8() V12() Element of NAT
S2 . 1 is set
S2 . 2 is set
S2 . 3 is set
<*(S2 . 1),(S2 . 2),(S2 . 3)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
rng S2 is Element of bool C1
bool C1 is non empty set
{(S2 . 1),(S2 . 2),(S2 . 3)} is non empty set
<*(S2 . 1),(S2 . 3)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(S2 . 1),(S2 . 3)*>] is V21() set
{0,<*(S2 . 1),(S2 . 3)*>} is functional non empty set
{{0,<*(S2 . 1),(S2 . 3)*>},{0}} is non empty set
B1 is V21() set
G is non empty set
2 -tuples_on G is functional non empty FinSequence-membered FinSequenceSet of G
<*(S2 . 1)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*(S2 . 1)*>] is V21() set
{1,<*(S2 . 1)*>} is non empty set
{{1,<*(S2 . 1)*>},{1}} is non empty set
<*(S2 . 1),(S2 . 1)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(S2 . 1),(S2 . 1)*>] is V21() set
{0,<*(S2 . 1),(S2 . 1)*>} is functional non empty set
{{0,<*(S2 . 1),(S2 . 1)*>},{0}} is non empty set
[2,<*(S2 . 1),(S2 . 2),(S2 . 3)*>] is V21() set
{2,<*(S2 . 1),(S2 . 2),(S2 . 3)*>} is non empty set
{{2,<*(S2 . 1),(S2 . 2),(S2 . 3)*>},{2}} is non empty set
S1 `1 is set
S1 is Relation-like Function-like set
proj1 S1 is set
proj2 S1 is set
[:([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):]),[:{0},(2 -tuples_on C1):]:] is Relation-like set
bool [:([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):]),[:{0},(2 -tuples_on C1):]:] is non empty set
F is Relation-like [:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] -defined [:{0},(2 -tuples_on C1):] * -valued Function-like total V36([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):],[:{0},(2 -tuples_on C1):] * ) Function-yielding V78() Element of bool [:([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):]),([:{0},(2 -tuples_on C1):] *):]
S2 is Relation-like [:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] -defined [:{0},(2 -tuples_on C1):] -valued Function-like V36([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):],[:{0},(2 -tuples_on C1):]) Element of bool [:([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):]),[:{0},(2 -tuples_on C1):]:]
ManySortedSign(# [:{0},(2 -tuples_on C1):],([:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):]),F,S2 #) is strict ManySortedSign
A1 is strict ManySortedSign
the carrier of A1 is set
the carrier' of A1 is set
the Arity of A1 is Relation-like the carrier' of A1 -defined the carrier of A1 * -valued Function-like total V36( the carrier' of A1, the carrier of A1 * ) Function-yielding V78() Element of bool [: the carrier' of A1,( the carrier of A1 *):]
the carrier of A1 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of A1
[: the carrier' of A1,( the carrier of A1 *):] is Relation-like set
bool [: the carrier' of A1,( the carrier of A1 *):] is non empty set
the ResultSort of A1 is Relation-like the carrier' of A1 -defined the carrier of A1 -valued Function-like V36( the carrier' of A1, the carrier of A1) Element of bool [: the carrier' of A1, the carrier of A1:]
[: the carrier' of A1, the carrier of A1:] is Relation-like set
bool [: the carrier' of A1, the carrier of A1:] is non empty set
A2 is set
f is non empty set
G is Element of f
<*G*> is Relation-like NAT -defined f -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of f
1 -tuples_on f is functional non empty FinSequence-membered FinSequenceSet of f
<*A2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*A2*>] is V21() set
{1,<*A2*>} is non empty set
{{1,<*A2*>},{1}} is non empty set
S2 . [1,<*A2*>] is set
B1 is set
H is set
o is set
<*B1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*B1*>] is V21() set
{1,<*B1*>} is non empty set
{{1,<*B1*>},{1}} is non empty set
<*B1,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*B1,B1*>] is V21() set
{0,<*B1,B1*>} is functional non empty set
{{0,<*B1,B1*>},{0}} is non empty set
<*B1,H,o*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*B1,H,o*>] is V21() set
{2,<*B1,H,o*>} is non empty set
{{2,<*B1,H,o*>},{2}} is non empty set
<*B1,o*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*B1,o*>] is V21() set
{0,<*B1,o*>} is functional non empty set
{{0,<*B1,o*>},{0}} is non empty set
F . [1,<*A2*>] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
the Arity of A1 . [1,<*A2*>] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
x is set
a is set
b is set
<*x*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*x*>] is V21() set
{1,<*x*>} is non empty set
{{1,<*x*>},{1}} is non empty set
<*x,a,b*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*x,a,b*>] is V21() set
{2,<*x,a,b*>} is non empty set
{{2,<*x,a,b*>},{2}} is non empty set
<*a,b*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*a,b*>] is V21() set
{0,<*a,b*>} is functional non empty set
{{0,<*a,b*>},{0}} is non empty set
<*x,a*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*x,a*>] is V21() set
{0,<*x,a*>} is functional non empty set
{{0,<*x,a*>},{0}} is non empty set
<*[0,<*a,b*>],[0,<*x,a*>]*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
<*A2*> . 1 is set
<*B1*> . 1 is set
the ResultSort of A1 . [1,<*A2*>] is set
<*A2,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A2,A2*>] is V21() set
{0,<*A2,A2*>} is functional non empty set
{{0,<*A2,A2*>},{0}} is non empty set
A2 is set
f is set
G is set
<*A2,f,G*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*A2,f,G*>] is V21() set
{2,<*A2,f,G*>} is non empty set
{{2,<*A2,f,G*>},{2}} is non empty set
the Arity of A1 . [2,<*A2,f,G*>] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
<*f,G*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*f,G*>] is V21() set
{0,<*f,G*>} is functional non empty set
{{0,<*f,G*>},{0}} is non empty set
<*A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A2,f*>] is V21() set
{0,<*A2,f*>} is functional non empty set
{{0,<*A2,f*>},{0}} is non empty set
<*[0,<*f,G*>],[0,<*A2,f*>]*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
the ResultSort of A1 . [2,<*A2,f,G*>] is set
<*A2,G*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A2,G*>] is V21() set
{0,<*A2,G*>} is functional non empty set
{{0,<*A2,G*>},{0}} is non empty set
B1 is non empty set
H is Element of B1
o is Element of B1
x is Element of B1
<*H,o,x*> is Relation-like NAT -defined B1 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of B1
3 -tuples_on B1 is functional non empty FinSequence-membered FinSequenceSet of B1
F . [2,<*A2,f,G*>] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
a is set
b is set
c is set
<*a*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*a*>] is V21() set
{1,<*a*>} is non empty set
{{1,<*a*>},{1}} is non empty set
<*a,b,c*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*a,b,c*>] is V21() set
{2,<*a,b,c*>} is non empty set
{{2,<*a,b,c*>},{2}} is non empty set
<*b,c*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*b,c*>] is V21() set
{0,<*b,c*>} is functional non empty set
{{0,<*b,c*>},{0}} is non empty set
<*a,b*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*a,b*>] is V21() set
{0,<*a,b*>} is functional non empty set
{{0,<*a,b*>},{0}} is non empty set
<*[0,<*b,c*>],[0,<*a,b*>]*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
<*A2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
<*f*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
<*A2*> ^ <*f*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
<*G*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
(<*A2*> ^ <*f*>) ^ <*G*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
<*b*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
<*a*> ^ <*b*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
<*c*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
(<*a*> ^ <*b*>) ^ <*c*> is Relation-like NAT -defined Function-like non empty V24() FinSequence-like FinSubsequence-like set
S2 . [2,<*A2,f,G*>] is set
g is set
h is set
gh is set
<*g*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*g*>] is V21() set
{1,<*g*>} is non empty set
{{1,<*g*>},{1}} is non empty set
<*g,g*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*g,g*>] is V21() set
{0,<*g,g*>} is functional non empty set
{{0,<*g,g*>},{0}} is non empty set
<*g,h,gh*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*g,h,gh*>] is V21() set
{2,<*g,h,gh*>} is non empty set
{{2,<*g,h,gh*>},{2}} is non empty set
<*g,gh*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*g,gh*>] is V21() set
{0,<*g,gh*>} is functional non empty set
{{0,<*g,gh*>},{0}} is non empty set
<*A2,f,G*> . 1 is set
<*g,h,gh*> . 1 is set
<*A2,f,G*> . 3 is set
C2 is strict ManySortedSign
the carrier of C2 is set
the carrier' of C2 is set
the Arity of C2 is Relation-like the carrier' of C2 -defined the carrier of C2 * -valued Function-like total V36( the carrier' of C2, the carrier of C2 * ) Function-yielding V78() Element of bool [: the carrier' of C2,( the carrier of C2 *):]
the carrier of C2 * is functional non empty FinSequence-membered FinSequenceSet of the carrier of C2
[: the carrier' of C2,( the carrier of C2 *):] is Relation-like set
bool [: the carrier' of C2,( the carrier of C2 *):] is non empty set
the ResultSort of C2 is Relation-like the carrier' of C2 -defined the carrier of C2 -valued Function-like V36( the carrier' of C2, the carrier of C2) Element of bool [: the carrier' of C2, the carrier of C2:]
[: the carrier' of C2, the carrier of C2:] is Relation-like set
bool [: the carrier' of C2, the carrier of C2:] is non empty set
F is strict ManySortedSign
the carrier of F is set
the carrier' of F is set
the Arity of F is Relation-like the carrier' of F -defined the carrier of F * -valued Function-like total V36( the carrier' of F, the carrier of F * ) Function-yielding V78() Element of bool [: the carrier' of F,( the carrier of F *):]
the carrier of F * is functional non empty FinSequence-membered FinSequenceSet of the carrier of F
[: the carrier' of F,( the carrier of F *):] is Relation-like set
bool [: the carrier' of F,( the carrier of F *):] is non empty set
the ResultSort of F is Relation-like the carrier' of F -defined the carrier of F -valued Function-like V36( the carrier' of F, the carrier of F) Element of bool [: the carrier' of F, the carrier of F:]
[: the carrier' of F, the carrier of F:] is Relation-like set
bool [: the carrier' of F, the carrier of F:] is non empty set
S1 is set
S1 `1 is set
S1 `2 is set
S2 is set
A1 is set
A2 is set
<*S2,A1,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,(S1 `2)] is V21() set
{2,(S1 `2)} is non empty set
{{2,(S1 `2)},{2}} is non empty set
the Arity of C2 . [2,(S1 `2)] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
<*A1,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A1,A2*>] is V21() set
{0,<*A1,A2*>} is functional non empty set
{{0,<*A1,A2*>},{0}} is non empty set
<*S2,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,A1*>] is V21() set
{0,<*S2,A1*>} is functional non empty set
{{0,<*S2,A1*>},{0}} is non empty set
<*[0,<*A1,A2*>],[0,<*S2,A1*>]*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
the Arity of F . [2,(S1 `2)] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[1,(S1 `2)] is V21() set
{1,(S1 `2)} is non empty set
{{1,(S1 `2)},{1}} is non empty set
the Arity of C2 . [1,(S1 `2)] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
the Arity of F . [1,(S1 `2)] is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
S2 is set
<*S2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
S2 is set
<*S2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[(S1 `1),(S1 `2)] is V21() set
{(S1 `1),(S1 `2)} is non empty set
{(S1 `1)} is non empty set
{{(S1 `1),(S1 `2)},{(S1 `1)}} is non empty set
the Arity of C2 . S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
the Arity of F . S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
S1 is set
S1 `1 is set
S1 `2 is set
S2 is set
A1 is set
A2 is set
<*S2,A1,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,(S1 `2)] is V21() set
{2,(S1 `2)} is non empty set
{{2,(S1 `2)},{2}} is non empty set
the ResultSort of C2 . [2,(S1 `2)] is set
<*S2,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,A2*>] is V21() set
{0,<*S2,A2*>} is functional non empty set
{{0,<*S2,A2*>},{0}} is non empty set
the ResultSort of F . [2,(S1 `2)] is set
S2 is set
<*S2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,(S1 `2)] is V21() set
{1,(S1 `2)} is non empty set
{{1,(S1 `2)},{1}} is non empty set
the ResultSort of C2 . [1,(S1 `2)] is set
<*S2,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,S2*>] is V21() set
{0,<*S2,S2*>} is functional non empty set
{{0,<*S2,S2*>},{0}} is non empty set
the ResultSort of F . [1,(S1 `2)] is set
[(S1 `1),(S1 `2)] is V21() set
{(S1 `1),(S1 `2)} is non empty set
{(S1 `1)} is non empty set
{{(S1 `1),(S1 `2)},{(S1 `1)}} is non empty set
the ResultSort of C2 . S1 is set
the ResultSort of F . S1 is set
dom the Arity of C2 is Element of bool the carrier' of C2
bool the carrier' of C2 is non empty set
dom the Arity of F is Element of bool the carrier' of F
bool the carrier' of F is non empty set
dom the ResultSort of C2 is Element of bool the carrier' of C2
dom the ResultSort of F is Element of bool the carrier' of F
C1 is set
(C1) is strict ManySortedSign
the carrier of (C1) is set
the carrier' of (C1) is set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
1 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
3 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like set
[:{2},(3 -tuples_on C1):] is Relation-like set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like set
C1 is non empty set
(C1) is strict feasible ManySortedSign
the carrier of (C1) is set
2 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like non empty set
the carrier' of (C1) is set
1 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like non empty set
3 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like non empty set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like non empty set
C1 is non empty feasible feasible ManySortedSign
the carrier of C1 is non empty set
C2 is set
(C2) is strict feasible ManySortedSign
2 -tuples_on C2 is functional FinSequence-membered FinSequenceSet of C2
[:{0},(2 -tuples_on C2):] is Relation-like set
the Element of the carrier of C1 is Element of the carrier of C1
S1 is set
S2 is set
[S1,S2] is V21() set
{S1,S2} is non empty set
{S1} is non empty set
{{S1,S2},{S1}} is non empty set
C2 * is functional non empty FinSequence-membered FinSequenceSet of C2
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like NAT -defined C2 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C2 * : len b<sub>1</sub> = 2 } is set
A1 is Relation-like NAT -defined C2 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C2 *
len A1 is V6() V7() V8() V12() Element of NAT
dom A1 is Element of bool NAT
A1 . 1 is set
rng A1 is Element of bool C2
bool C2 is non empty set
A2 is non empty set
the carrier' of (C2) is set
1 -tuples_on C2 is functional FinSequence-membered FinSequenceSet of C2
[:{1},(1 -tuples_on C2):] is Relation-like set
3 -tuples_on C2 is functional FinSequence-membered FinSequenceSet of C2
[:{2},(3 -tuples_on C2):] is Relation-like set
[:{1},(1 -tuples_on C2):] \/ [:{2},(3 -tuples_on C2):] is Relation-like set
f is Element of A2
<*f*> is Relation-like NAT -defined A2 -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of A2
1 -tuples_on A2 is functional non empty FinSequence-membered FinSequenceSet of A2
the carrier' of C1 is set
({{}}) is non empty non void feasible strict feasible ManySortedSign
C1 is non empty non void feasible strict feasible ManySortedSign
the carrier of C1 is non empty set
2 -tuples_on {{}} is functional non empty FinSequence-membered FinSequenceSet of {{}}
[:{0},(2 -tuples_on {{}}):] is Relation-like non empty set
C1 is set
(C1) is strict feasible ManySortedSign
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
the carrier of (C1) is set
F is feasible () ManySortedSign
the carrier of F is set
C1 is set
C2 is set
F is feasible (C1)
(C2) is strict feasible ManySortedSign
the carrier of F is set
2 -tuples_on C2 is functional FinSequence-membered FinSequenceSet of C2
[:{0},(2 -tuples_on C2):] is Relation-like set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
S1 is set
<*S1,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
S1 is set
<*S1,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
C1 is set
C2 is feasible (C1)
(C1) is strict feasible ManySortedSign
the carrier of C2 is set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
C1 is non empty set
C2 is feasible () (C1)
(C1) is non empty non void feasible strict feasible ManySortedSign
the carrier of (C1) is non empty set
the carrier of C2 is set
C1 is set
(C1) is strict feasible ManySortedSign
the carrier of (C1) is set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
C1 is set
(C1) is strict feasible ManySortedSign
the carrier of (C1) is set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
C1 is ManySortedSign
the carrier of C1 is set
the carrier' of C1 is set
the carrier of C1 \/ the carrier' of C1 is set
proj2 ( the carrier of C1 \/ the carrier' of C1) is set
SubFuncs (proj2 ( the carrier of C1 \/ the carrier' of C1)) is set
union (SubFuncs (proj2 ( the carrier of C1 \/ the carrier' of C1))) is set
proj2 (union (SubFuncs (proj2 ( the carrier of C1 \/ the carrier' of C1)))) is set
F is set
S1 is set
S2 is set
[S2,S1] is V21() set
{S2,S1} is non empty set
{S2} is non empty set
{{S2,S1},{S2}} is non empty set
A1 is set
A2 is Relation-like Function-like set
f is set
[f,A2] is V21() set
{f,A2} is non empty set
{f} is non empty set
{{f,A2},{f}} is non empty set
G is set
B1 is Relation-like Function-like set
[G,B1] is V21() set
{G,B1} is non empty set
{G} is non empty set
{{G,B1},{G}} is non empty set
proj2 B1 is set
S2 is set
A1 is Relation-like Function-like set
[S2,A1] is V21() set
{S2,A1} is non empty set
{S2} is non empty set
{{S2,A1},{S2}} is non empty set
proj2 A1 is set
A2 is set
[A2,S1] is V21() set
{A2,S1} is non empty set
{A2} is non empty set
{{A2,S1},{A2}} is non empty set
C1 is set
(C1) is strict feasible () (C1)
((C1)) is set
the carrier' of (C1) is set
1 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like set
3 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like set
F is set
the carrier of (C1) is set
the carrier of (C1) \/ the carrier' of (C1) is set
S1 is set
S2 is Relation-like Function-like set
[S1,S2] is V21() set
{S1,S2} is non empty set
{S1} is non empty set
{{S1,S2},{S1}} is non empty set
proj2 S2 is set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
F is set
<*F,F*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*F,F*>] is V21() set
{0,<*F,F*>} is functional non empty set
{{0,<*F,F*>},{0}} is non empty set
proj2 <*F,F*> is non empty set
{F,F} is non empty set
[:NAT,NAT:] is Relation-like non empty set
bool [:NAT,NAT:] is non empty set
C1 is set
(C1) is strict feasible () (C1)
A1 is set
F is set
S1 is set
S2 is set
F is set
F is Relation-like Function-like set
proj1 F is set
proj2 F is set
S1 is Relation-like NAT -defined NAT -valued Function-like non empty total V36( NAT , NAT ) Element of bool [:NAT,NAT:]
the carrier of (C1) is set
((C1)) is set
the carrier' of (C1) is set
2 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like set
S2 is set
A1 is set
A2 is set
[A1,A2] is V21() set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
f is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
G is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() Element of NAT
S1 . G is V6() V7() V8() V12() Element of NAT
B1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[G,B1] is V21() set
{G,B1} is functional non empty set
{G} is functional non empty set
{{G,B1},{G}} is non empty set
len B1 is V6() V7() V8() V12() Element of NAT
(S1 . G) -tuples_on ((C1)) is functional FinSequence-membered FinSequenceSet of ((C1))
[:{G},((S1 . G) -tuples_on ((C1))):] is Relation-like set
S2 is set
1 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like set
3 -tuples_on C1 is functional FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like set
A1 is set
A2 is set
[A1,A2] is V21() set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
G is V6() V7() V8() V12() non empty Element of NAT
S1 . G is V6() V7() V8() V12() Element of NAT
{G} is non empty set
(S1 . G) -tuples_on ((C1)) is functional FinSequence-membered FinSequenceSet of ((C1))
[:{G},((S1 . G) -tuples_on ((C1))):] is Relation-like set
f is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of C1
[G,f] is V21() set
{G,f} is non empty set
{{G,f},{G}} is non empty set
len f is V6() V7() V8() V12() Element of NAT
A1 is set
A2 is set
[A1,A2] is V21() set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
G is V6() V7() V8() V12() non empty Element of NAT
S1 . G is V6() V7() V8() V12() Element of NAT
{G} is non empty set
(S1 . G) -tuples_on ((C1)) is functional FinSequence-membered FinSequenceSet of ((C1))
[:{G},((S1 . G) -tuples_on ((C1))):] is Relation-like set
f is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like FinSequence of C1
[G,f] is V21() set
{G,f} is non empty set
{{G,f},{G}} is non empty set
len f is V6() V7() V8() V12() Element of NAT
({{}}) is non empty non void feasible strict feasible () () ({{}})
C1 is set
(C1) is strict feasible () () (C1)
C1 is () ManySortedSign
the carrier of C1 is set
the carrier' of C1 is set
(C1) is set
C2 is set
the carrier of C1 \/ the carrier' of C1 is set
F is Relation-like NAT -defined NAT -valued Function-like non empty total V36( NAT , NAT ) Element of bool [:NAT,NAT:]
S1 is V6() V7() V8() V12() Element of NAT
S2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[S1,S2] is V21() set
{S1,S2} is non empty set
{S1} is non empty set
{{S1,S2},{S1}} is non empty set
len S2 is V6() V7() V8() V12() Element of NAT
F . S1 is V6() V7() V8() V12() Element of NAT
(F . S1) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{S1},((F . S1) -tuples_on (C1)):] is Relation-like set
proj2 S2 is set
A1 is set
S1 is V6() V7() V8() V12() Element of NAT
S2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[S1,S2] is V21() set
{S1,S2} is non empty set
{S1} is non empty set
{{S1,S2},{S1}} is non empty set
len S2 is V6() V7() V8() V12() Element of NAT
F . S1 is V6() V7() V8() V12() Element of NAT
(F . S1) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{S1},((F . S1) -tuples_on (C1)):] is Relation-like set
proj2 S2 is set
A1 is set
C1 is () ManySortedSign
the carrier of C1 is set
the carrier' of C1 is set
C2 is set
F is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[C2,F] is V21() set
{C2,F} is non empty set
{C2} is non empty set
{{C2,F},{C2}} is non empty set
S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[C2,S1] is V21() set
{C2,S1} is non empty set
{{C2,S1},{C2}} is non empty set
len F is V6() V7() V8() V12() Element of NAT
len S1 is V6() V7() V8() V12() Element of NAT
(C1) is set
S2 is Relation-like NAT -defined NAT -valued Function-like non empty total V36( NAT , NAT ) Element of bool [:NAT,NAT:]
A1 is V6() V7() V8() V12() Element of NAT
A2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[A1,A2] is V21() set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
len A2 is V6() V7() V8() V12() Element of NAT
S2 . A1 is V6() V7() V8() V12() Element of NAT
(S2 . A1) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{A1},((S2 . A1) -tuples_on (C1)):] is Relation-like set
f is V6() V7() V8() V12() Element of NAT
G is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[f,G] is V21() set
{f,G} is non empty set
{f} is non empty set
{{f,G},{f}} is non empty set
len G is V6() V7() V8() V12() Element of NAT
S2 . f is V6() V7() V8() V12() Element of NAT
(S2 . f) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{f},((S2 . f) -tuples_on (C1)):] is Relation-like set
A1 is V6() V7() V8() V12() Element of NAT
A2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[A1,A2] is V21() set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
len A2 is V6() V7() V8() V12() Element of NAT
S2 . A1 is V6() V7() V8() V12() Element of NAT
(S2 . A1) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{A1},((S2 . A1) -tuples_on (C1)):] is Relation-like set
f is V6() V7() V8() V12() Element of NAT
G is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[f,G] is V21() set
{f,G} is non empty set
{f} is non empty set
{{f,G},{f}} is non empty set
len G is V6() V7() V8() V12() Element of NAT
S2 . f is V6() V7() V8() V12() Element of NAT
(S2 . f) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{f},((S2 . f) -tuples_on (C1)):] is Relation-like set
C1 is () ManySortedSign
(C1) is set
the carrier of C1 is set
the carrier' of C1 is set
C2 is set
S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
len S1 is V6() V7() V8() V12() Element of NAT
F is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
len F is V6() V7() V8() V12() Element of NAT
proj2 S1 is set
[C2,F] is V21() set
{C2,F} is non empty set
{C2} is non empty set
{{C2,F},{C2}} is non empty set
[C2,S1] is V21() set
{C2,S1} is non empty set
{{C2,S1},{C2}} is non empty set
S2 is Relation-like NAT -defined NAT -valued Function-like non empty total V36( NAT , NAT ) Element of bool [:NAT,NAT:]
A1 is V6() V7() V8() V12() Element of NAT
A2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[A1,A2] is V21() set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
len A2 is V6() V7() V8() V12() Element of NAT
S2 . A1 is V6() V7() V8() V12() Element of NAT
(S2 . A1) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{A1},((S2 . A1) -tuples_on (C1)):] is Relation-like set
A1 is V6() V7() V8() V12() Element of NAT
A2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[A1,A2] is V21() set
{A1,A2} is non empty set
{A1} is non empty set
{{A1,A2},{A1}} is non empty set
len A2 is V6() V7() V8() V12() Element of NAT
S2 . A1 is V6() V7() V8() V12() Element of NAT
(S2 . A1) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{A1},((S2 . A1) -tuples_on (C1)):] is Relation-like set
C1 is non empty non void feasible feasible () () ManySortedSign
(C1) is set
the carrier of C1 is non empty set
the Element of the carrier of C1 is Element of the carrier of C1
F is set
(F) is strict feasible () () (F)
2 -tuples_on F is functional FinSequence-membered FinSequenceSet of F
[:{0},(2 -tuples_on F):] is Relation-like set
the carrier' of C1 is non empty set
S1 is Relation-like NAT -defined NAT -valued Function-like non empty total V36( NAT , NAT ) Element of bool [:NAT,NAT:]
S2 is V6() V7() V8() V12() Element of NAT
A1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[S2,A1] is V21() set
{S2,A1} is non empty set
{S2} is non empty set
{{S2,A1},{S2}} is non empty set
len A1 is V6() V7() V8() V12() Element of NAT
S1 . S2 is V6() V7() V8() V12() Element of NAT
(S1 . S2) -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
[:{S2},((S1 . S2) -tuples_on (C1)):] is Relation-like set
A2 is set
<*A2,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A2,A2*>] is V21() set
{0,<*A2,A2*>} is functional non empty set
{{0,<*A2,A2*>},{0}} is non empty set
the carrier of C1 \/ the carrier' of C1 is non empty set
proj2 <*A2,A2*> is non empty set
{A2,A2} is non empty set
2 -tuples_on (C1) is functional FinSequence-membered FinSequenceSet of (C1)
A2 is set
<*A2,A2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
C1 is non empty non void feasible feasible () ManySortedSign
the carrier of C1 is non empty set
C2 is Element of the carrier of C1
C2 `2 is set
F is set
(F) is strict feasible () () (F)
2 -tuples_on F is functional FinSequence-membered FinSequenceSet of F
[:{0},(2 -tuples_on F):] is Relation-like set
C1 is non empty feasible feasible () ManySortedSign
the carrier of C1 is non empty set
C2 is Element of the carrier of C1
C2 `2 is set
(C1) is set
F is V6() V7() V8() V12() Element of NAT
S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[F,S1] is V21() set
{F,S1} is non empty set
{F} is non empty set
{{F,S1},{F}} is non empty set
proj2 S1 is set
C1 is non void () ManySortedSign
the carrier' of C1 is non empty set
C2 is Element of the carrier' of C1
C2 `2 is set
(C1) is set
F is V6() V7() V8() V12() Element of NAT
S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[F,S1] is V21() set
{F,S1} is non empty set
{F} is non empty set
{{F,S1},{F}} is non empty set
proj2 S1 is set
C1 is non empty non void feasible feasible () ManySortedSign
the carrier of C1 is non empty set
C2 is Element of the carrier of C1
C2 `2 is Relation-like Function-like set
F is set
(F) is strict feasible () () (F)
2 -tuples_on F is functional FinSequence-membered FinSequenceSet of F
[:{0},(2 -tuples_on F):] is Relation-like set
S1 is set
S2 is set
<*S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
C1 is non empty feasible feasible () ManySortedSign
the carrier of C1 is non empty set
C2 is Element of the carrier of C1
C2 `2 is Relation-like Function-like set
(C1) is set
F is V6() V7() V8() V12() Element of NAT
S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[F,S1] is V21() set
{F,S1} is non empty set
{F} is non empty set
{{F,S1},{F}} is non empty set
proj2 S1 is set
C1 is non void () ManySortedSign
the carrier' of C1 is non empty set
C2 is Element of the carrier' of C1
C2 `2 is Relation-like Function-like set
(C1) is set
F is V6() V7() V8() V12() Element of NAT
S1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
[F,S1] is V21() set
{F,S1} is non empty set
{F} is non empty set
{{F,S1},{F}} is non empty set
proj2 S1 is set
C1 is set
<*C1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*C1*>] is V21() set
{1,<*C1*>} is non empty set
{{1,<*C1*>},{1}} is non empty set
C2 is set
<*C1,C2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*C1,C2*>] is V21() set
{0,<*C1,C2*>} is functional non empty set
{{0,<*C1,C2*>},{0}} is non empty set
F is set
<*C1,C2,F*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C1,C2,F*>] is V21() set
{2,<*C1,C2,F*>} is non empty set
{{2,<*C1,C2,F*>},{2}} is non empty set
C1 is non empty set
C2 is non empty non void feasible feasible () (C1)
the carrier' of C2 is non empty set
the carrier of C2 is non empty set
F is Element of C1
(F) is set
<*F*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*F*>] is V21() set
{1,<*F*>} is non empty set
{{1,<*F*>},{1}} is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
the carrier' of (C1) is non empty set
1 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like non empty set
3 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like non empty set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like non empty set
the carrier of (C1) is non empty set
<*F*> is Relation-like NAT -defined C1 -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of C1
[1,<*F*>] is V21() set
{1,<*F*>} is non empty set
{{1,<*F*>},{1}} is non empty set
S1 is Element of C1
(F,S1) is set
<*F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*F,S1*>] is V21() set
{0,<*F,S1*>} is functional non empty set
{{0,<*F,S1*>},{0}} is non empty set
2 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like non empty set
<*F,S1*> is Relation-like NAT -defined C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of C1
[0,<*F,S1*>] is V21() set
{0,<*F,S1*>} is functional non empty set
{{0,<*F,S1*>},{0}} is non empty set
S2 is Element of C1
(F,S1,S2) is set
<*F,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*F,S1,S2*>] is V21() set
{2,<*F,S1,S2*>} is non empty set
{{2,<*F,S1,S2*>},{2}} is non empty set
<*F,S1,S2*> is Relation-like NAT -defined C1 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of C1
[2,<*F,S1,S2*>] is V21() set
{2,<*F,S1,S2*>} is non empty set
{{2,<*F,S1,S2*>},{2}} is non empty set
C1 is non empty set
C2 is Element of C1
(C2) is set
<*C2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*C2*>] is V21() set
{1,<*C2*>} is non empty set
{{1,<*C2*>},{1}} is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
the carrier' of (C1) is non empty set
F is Element of C1
(C2,F) is set
<*C2,F*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*C2,F*>] is V21() set
{0,<*C2,F*>} is functional non empty set
{{0,<*C2,F*>},{0}} is non empty set
the carrier of (C1) is non empty set
S1 is Element of C1
(C2,F,S1) is set
<*C2,F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,S1*>] is V21() set
{2,<*C2,F,S1*>} is non empty set
{{2,<*C2,F,S1*>},{2}} is non empty set
C1 is set
(C1) is set
<*C1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*C1*>] is V21() set
{1,<*C1*>} is non empty set
{{1,<*C1*>},{1}} is non empty set
C2 is set
(C2) is set
<*C2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*C2*>] is V21() set
{1,<*C2*>} is non empty set
{{1,<*C2*>},{1}} is non empty set
C1 is set
F is set
(C1,F) is set
<*C1,F*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*C1,F*>] is V21() set
{0,<*C1,F*>} is functional non empty set
{{0,<*C1,F*>},{0}} is non empty set
C2 is set
S1 is set
(C2,S1) is set
<*C2,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*C2,S1*>] is V21() set
{0,<*C2,S1*>} is functional non empty set
{{0,<*C2,S1*>},{0}} is non empty set
<*C1,F*> . 1 is set
<*C1,F*> . 2 is set
C1 is set
F is set
S2 is set
(C1,F,S2) is set
<*C1,F,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C1,F,S2*>] is V21() set
{2,<*C1,F,S2*>} is non empty set
{{2,<*C1,F,S2*>},{2}} is non empty set
C2 is set
S1 is set
A1 is set
(C2,S1,A1) is set
<*C2,S1,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,S1,A1*>] is V21() set
{2,<*C2,S1,A1*>} is non empty set
{{2,<*C2,S1,A1*>},{2}} is non empty set
<*C1,F,S2*> . 3 is set
<*C1,F,S2*> . 1 is set
<*C1,F,S2*> . 2 is set
C1 is non empty set
C2 is non empty non void feasible feasible () (C1)
the carrier of C2 is non empty set
F is Element of the carrier of C2
2 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{0},(2 -tuples_on C1):] is Relation-like non empty set
F `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
C1 * is functional non empty FinSequence-membered FinSequenceSet of C1
{ b₁ where b₁ is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 * : len b₁ = 2 } is set
S1 is Relation-like NAT -defined C1 -valued Function-like V24() FinSequence-like FinSubsequence-like Element of C1 *
len S1 is V6() V7() V8() V12() Element of NAT
S1 . 1 is set
S1 . 2 is set
{(S1 . 1),(S1 . 2)} is non empty set
<*(S1 . 1),(S1 . 2)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
rng S1 is Element of bool C1
bool C1 is non empty set
S2 is Element of C1
A1 is Element of C1
(C1,S2,A1) is Element of the carrier of (C1)
(C1) is non empty non void feasible strict feasible () () (C1)
the carrier of (C1) is non empty set
<*S2,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,A1*>] is V21() set
{0,<*S2,A1*>} is functional non empty set
{{0,<*S2,A1*>},{0}} is non empty set
F `1 is set
[(F `1),(F `2)] is V21() set
{(F `1),(F `2)} is non empty set
{(F `1)} is non empty set
{{(F `1),(F `2)},{(F `1)}} is non empty set
C1 is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
the carrier' of (C1) is non empty set
C2 is Element of the carrier' of (C1)
C2 `1 is set
C2 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
len (C2 `2) is V6() V7() V8() V12() Element of NAT
1 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like non empty set
3 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like non empty set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like non empty set
C1 is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
the carrier' of (C1) is non empty set
C2 is Element of the carrier' of (C1)
C2 `1 is set
C2 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
len (C2 `2) is V6() V7() V8() V12() Element of NAT
1 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like non empty set
3 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like non empty set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like non empty set
[(C2 `1),(C2 `2)] is V21() set
{(C2 `1),(C2 `2)} is non empty set
{(C2 `1)} is non empty set
{{(C2 `1),(C2 `2)},{(C2 `1)}} is non empty set
F is set
<*F*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
S1 is Element of C1
(C1,S1) is Element of the carrier' of (C1)
<*S1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*S1*>] is V21() set
{1,<*S1*>} is non empty set
{{1,<*S1*>},{1}} is non empty set
C1 is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
the carrier' of (C1) is non empty set
C2 is Element of the carrier' of (C1)
C2 `1 is set
C2 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
len (C2 `2) is V6() V7() V8() V12() Element of NAT
1 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{1},(1 -tuples_on C1):] is Relation-like non empty set
3 -tuples_on C1 is functional non empty FinSequence-membered FinSequenceSet of C1
[:{2},(3 -tuples_on C1):] is Relation-like non empty set
[:{1},(1 -tuples_on C1):] \/ [:{2},(3 -tuples_on C1):] is Relation-like non empty set
[(C2 `1),(C2 `2)] is V21() set
{(C2 `1),(C2 `2)} is non empty set
{(C2 `1)} is non empty set
{{(C2 `1),(C2 `2)},{(C2 `1)}} is non empty set
F is set
S1 is set
S2 is set
<*F,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
A1 is Element of C1
A2 is Element of C1
f is Element of C1
(C1,A1,A2,f) is Element of the carrier' of (C1)
<*A1,A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*A1,A2,f*>] is V21() set
{2,<*A1,A2,f*>} is non empty set
{{2,<*A1,A2,f*>},{2}} is non empty set
C1 is non empty set
F is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
C2 is Element of C1
(C1,C2) is Element of the carrier' of (C1)
the carrier' of (C1) is non empty set
<*C2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*C2*>] is V21() set
{1,<*C2*>} is non empty set
{{1,<*C2*>},{1}} is non empty set
the_arity_of (C1,C2) is Relation-like NAT -defined the carrier of (C1) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (C1) *
the carrier of (C1) is non empty set
the carrier of (C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of (C1)
the Arity of (C1) is Relation-like the carrier' of (C1) -defined the carrier of (C1) * -valued Function-like non empty total V36( the carrier' of (C1), the carrier of (C1) * ) Function-yielding V78() Element of bool [: the carrier' of (C1),( the carrier of (C1) *):]
[: the carrier' of (C1),( the carrier of (C1) *):] is Relation-like non empty set
bool [: the carrier' of (C1),( the carrier of (C1) *):] is non empty set
the Arity of (C1) . (C1,C2) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (C1) *
(F) is non empty non void feasible strict feasible () () (F)
S1 is Element of F
(F,S1) is Element of the carrier' of (F)
the carrier' of (F) is non empty set
<*S1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*S1*>] is V21() set
{1,<*S1*>} is non empty set
{{1,<*S1*>},{1}} is non empty set
the_result_sort_of (F,S1) is Element of the carrier of (F)
the carrier of (F) is non empty set
the ResultSort of (F) is Relation-like the carrier' of (F) -defined the carrier of (F) -valued Function-like non empty total V36( the carrier' of (F), the carrier of (F)) Element of bool [: the carrier' of (F), the carrier of (F):]
[: the carrier' of (F), the carrier of (F):] is Relation-like non empty set
bool [: the carrier' of (F), the carrier of (F):] is non empty set
the ResultSort of (F) . (F,S1) is Element of the carrier of (F)
(F,S1,S1) is Element of the carrier of (F)
<*S1,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S1,S1*>] is V21() set
{0,<*S1,S1*>} is functional non empty set
{{0,<*S1,S1*>},{0}} is non empty set
C1 is non empty set
S2 is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
C2 is Element of C1
F is Element of C1
S1 is Element of C1
(C1,C2,F,S1) is Element of the carrier' of (C1)
the carrier' of (C1) is non empty set
<*C2,F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,S1*>] is V21() set
{2,<*C2,F,S1*>} is non empty set
{{2,<*C2,F,S1*>},{2}} is non empty set
the_arity_of (C1,C2,F,S1) is Relation-like NAT -defined the carrier of (C1) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (C1) *
the carrier of (C1) is non empty set
the carrier of (C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of (C1)
the Arity of (C1) is Relation-like the carrier' of (C1) -defined the carrier of (C1) * -valued Function-like non empty total V36( the carrier' of (C1), the carrier of (C1) * ) Function-yielding V78() Element of bool [: the carrier' of (C1),( the carrier of (C1) *):]
[: the carrier' of (C1),( the carrier of (C1) *):] is Relation-like non empty set
bool [: the carrier' of (C1),( the carrier of (C1) *):] is non empty set
the Arity of (C1) . (C1,C2,F,S1) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (C1) *
(C1,F,S1) is Element of the carrier of (C1)
<*F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*F,S1*>] is V21() set
{0,<*F,S1*>} is functional non empty set
{{0,<*F,S1*>},{0}} is non empty set
(C1,C2,F) is Element of the carrier of (C1)
<*C2,F*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*C2,F*>] is V21() set
{0,<*C2,F*>} is functional non empty set
{{0,<*C2,F*>},{0}} is non empty set
<*(C1,F,S1),(C1,C2,F)*> is Relation-like NAT -defined the carrier of (C1) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (C1)
(S2) is non empty non void feasible strict feasible () () (S2)
A1 is Element of S2
A2 is Element of S2
f is Element of S2
(S2,A1,A2,f) is Element of the carrier' of (S2)
the carrier' of (S2) is non empty set
<*A1,A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*A1,A2,f*>] is V21() set
{2,<*A1,A2,f*>} is non empty set
{{2,<*A1,A2,f*>},{2}} is non empty set
the_result_sort_of (S2,A1,A2,f) is Element of the carrier of (S2)
the carrier of (S2) is non empty set
the ResultSort of (S2) is Relation-like the carrier' of (S2) -defined the carrier of (S2) -valued Function-like non empty total V36( the carrier' of (S2), the carrier of (S2)) Element of bool [: the carrier' of (S2), the carrier of (S2):]
[: the carrier' of (S2), the carrier of (S2):] is Relation-like non empty set
bool [: the carrier' of (S2), the carrier of (S2):] is non empty set
the ResultSort of (S2) . (S2,A1,A2,f) is Element of the carrier of (S2)
(S2,A1,f) is Element of the carrier of (S2)
<*A1,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A1,f*>] is V21() set
{0,<*A1,f*>} is functional non empty set
{{0,<*A1,f*>},{0}} is non empty set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier of ( the carrier of C1) is non empty set
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
the carrier of ( the carrier of C2) is non empty set
[: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
S1 is Relation-like the carrier of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):]
S2 is Relation-like the carrier of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):]
A1 is Element of the carrier of ( the carrier of C1)
S1 . A1 is Element of the carrier of ( the carrier of C2)
A1 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
(A1 `2) * (Obj F) is Relation-like NAT -defined the carrier of C2 -valued Function-like set
[0,((A1 `2) * (Obj F))] is V21() set
{0,((A1 `2) * (Obj F))} is functional non empty set
{{0,((A1 `2) * (Obj F))},{0}} is non empty set
S2 . A1 is Element of the carrier of ( the carrier of C2)
S1 is Relation-like Function-like set
proj1 S1 is set
proj2 S1 is set
S2 is set
A1 is set
S1 . A1 is set
2 -tuples_on the carrier of C1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C1
[:{0},(2 -tuples_on the carrier of C1):] is Relation-like non empty set
A2 is Element of the carrier of ( the carrier of C1)
A2 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
f is set
G is set
<*f,G*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
B1 is Element of the carrier of C1
H is Element of the carrier of C1
<*B1,H*> is Relation-like NAT -defined the carrier of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of C1
rng <*B1,H*> is non empty Element of bool the carrier of C1
bool the carrier of C1 is non empty set
dom (Obj F) is non empty Element of bool the carrier of C1
(Obj F) * <*B1,H*> is Relation-like NAT -defined the carrier of C2 -valued Function-like Element of bool [:NAT, the carrier of C2:]
[:NAT, the carrier of C2:] is Relation-like non empty set
bool [:NAT, the carrier of C2:] is non empty set
dom ((Obj F) * <*B1,H*>) is Element of bool NAT
dom <*B1,H*> is non empty Element of bool NAT
<*B1,H*> . 1 is set
o is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
o . 1 is set
(Obj F) . B1 is Element of the carrier of C2
2 -tuples_on the carrier of C2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C2
[:{0},(2 -tuples_on the carrier of C2):] is Relation-like non empty set
<*B1,H*> . 2 is set
o . 2 is set
(Obj F) . H is Element of the carrier of C2
len o is V6() V7() V8() V12() Element of NAT
<*((Obj F) . B1),((Obj F) . H)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
[0,o] is V21() set
{0,o} is functional non empty set
{{0,o},{0}} is non empty set
the carrier' of ( the carrier of C1) is non empty set
the carrier' of ( the carrier of C2) is non empty set
[: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is non empty set
S1 is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
S2 is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
A1 is Element of the carrier' of ( the carrier of C1)
S1 . A1 is Element of the carrier' of ( the carrier of C2)
A1 `1 is set
A1 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
(A1 `2) * (Obj F) is Relation-like NAT -defined the carrier of C2 -valued Function-like set
[(A1 `1),((A1 `2) * (Obj F))] is V21() set
{(A1 `1),((A1 `2) * (Obj F))} is non empty set
{(A1 `1)} is non empty set
{{(A1 `1),((A1 `2) * (Obj F))},{(A1 `1)}} is non empty set
S2 . A1 is Element of the carrier' of ( the carrier of C2)
S1 is Relation-like Function-like set
proj1 S1 is set
proj2 S1 is set
S2 is set
A1 is set
S1 . A1 is set
1 -tuples_on the carrier of C1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C1
[:{1},(1 -tuples_on the carrier of C1):] is Relation-like non empty set
3 -tuples_on the carrier of C1 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C1
[:{2},(3 -tuples_on the carrier of C1):] is Relation-like non empty set
[:{1},(1 -tuples_on the carrier of C1):] \/ [:{2},(3 -tuples_on the carrier of C1):] is Relation-like non empty set
A2 is Element of the carrier' of ( the carrier of C1)
A2 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
f is set
<*f*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
G is Element of the carrier of C1
<*G*> is Relation-like NAT -defined the carrier of C1 -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of C1
rng <*G*> is non empty Element of bool the carrier of C1
bool the carrier of C1 is non empty set
dom (Obj F) is non empty Element of bool the carrier of C1
(Obj F) * <*G*> is Relation-like NAT -defined the carrier of C2 -valued Function-like Element of bool [:NAT, the carrier of C2:]
[:NAT, the carrier of C2:] is Relation-like non empty set
bool [:NAT, the carrier of C2:] is non empty set
dom ((Obj F) * <*G*>) is Element of bool NAT
dom <*G*> is non empty Element of bool NAT
B1 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
len B1 is V6() V7() V8() V12() Element of NAT
<*G*> . 1 is set
B1 . 1 is set
(Obj F) . G is Element of the carrier of C2
<*((Obj F) . G)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
1 -tuples_on the carrier of C2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C2
[1,B1] is V21() set
{1,B1} is non empty set
{{1,B1},{1}} is non empty set
[:{1},(1 -tuples_on the carrier of C2):] is Relation-like non empty set
A2 `1 is set
3 -tuples_on the carrier of C2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C2
[:{2},(3 -tuples_on the carrier of C2):] is Relation-like non empty set
[:{1},(1 -tuples_on the carrier of C2):] \/ [:{2},(3 -tuples_on the carrier of C2):] is Relation-like non empty set
A2 is Element of the carrier' of ( the carrier of C1)
A2 `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
f is set
G is set
B1 is set
<*f,G,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
H is Element of the carrier of C1
o is Element of the carrier of C1
x is Element of the carrier of C1
<*H,o,x*> is Relation-like NAT -defined the carrier of C1 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of C1
rng <*H,o,x*> is non empty Element of bool the carrier of C1
bool the carrier of C1 is non empty set
dom (Obj F) is non empty Element of bool the carrier of C1
(Obj F) * <*H,o,x*> is Relation-like NAT -defined the carrier of C2 -valued Function-like Element of bool [:NAT, the carrier of C2:]
[:NAT, the carrier of C2:] is Relation-like non empty set
bool [:NAT, the carrier of C2:] is non empty set
dom ((Obj F) * <*H,o,x*>) is Element of bool NAT
dom <*H,o,x*> is non empty Element of bool NAT
<*H,o,x*> . 1 is set
a is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
a . 1 is set
(Obj F) . H is Element of the carrier of C2
<*H,o,x*> . 3 is set
a . 3 is set
(Obj F) . x is Element of the carrier of C2
<*H,o,x*> . 2 is set
a . 2 is set
(Obj F) . o is Element of the carrier of C2
len a is V6() V7() V8() V12() Element of NAT
<*((Obj F) . H),((Obj F) . o),((Obj F) . x)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
3 -tuples_on the carrier of C2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C2
[2,a] is V21() set
{2,a} is non empty set
{{2,a},{2}} is non empty set
[:{2},(3 -tuples_on the carrier of C2):] is Relation-like non empty set
A2 `1 is set
1 -tuples_on the carrier of C2 is functional non empty FinSequence-membered FinSequenceSet of the carrier of C2
[:{1},(1 -tuples_on the carrier of C2):] is Relation-like non empty set
[:{1},(1 -tuples_on the carrier of C2):] \/ [:{2},(3 -tuples_on the carrier of C2):] is Relation-like non empty set
A2 is Element of the carrier' of ( the carrier of C1)
C1 is set
C2 is Relation-like Function-like set
proj1 C2 is set
<*C1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
proj2 <*C1*> is non empty set
{C1} is non empty set
<*C1*> * C2 is Relation-like NAT -defined Function-like set
dom (<*C1*> * C2) is Element of bool NAT
dom <*C1*> is non empty Element of bool NAT
F is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
len F is V6() V7() V8() V12() Element of NAT
<*C1*> . 1 is set
F . 1 is set
C2 . C1 is set
<*(C2 . C1)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier of ( the carrier of C1) is non empty set
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
the carrier of ( the carrier of C2) is non empty set
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
(C1,C2,F) is Relation-like the carrier of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):]
[: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
S1 is Element of the carrier of C1
S2 is Element of the carrier of C1
( the carrier of C1,S1,S2) is Element of the carrier of ( the carrier of C1)
<*S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S1,S2*>] is V21() set
{0,<*S1,S2*>} is functional non empty set
{{0,<*S1,S2*>},{0}} is non empty set
(C1,C2,F) . ( the carrier of C1,S1,S2) is Element of the carrier of ( the carrier of C2)
F . S1 is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . S1 is Element of the carrier of C2
F . S2 is Element of the carrier of C2
(Obj F) . S2 is Element of the carrier of C2
( the carrier of C2,(F . S1),(F . S2)) is Element of the carrier of ( the carrier of C2)
<*(F . S1),(F . S2)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . S1),(F . S2)*>] is V21() set
{0,<*(F . S1),(F . S2)*>} is functional non empty set
{{0,<*(F . S1),(F . S2)*>},{0}} is non empty set
dom (Obj F) is non empty Element of bool the carrier of C1
bool the carrier of C1 is non empty set
( the carrier of C1,S1,S2) `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
(( the carrier of C1,S1,S2) `2) * (Obj F) is Relation-like NAT -defined the carrier of C2 -valued Function-like set
[0,((( the carrier of C1,S1,S2) `2) * (Obj F))] is V21() set
{0,((( the carrier of C1,S1,S2) `2) * (Obj F))} is functional non empty set
{{0,((( the carrier of C1,S1,S2) `2) * (Obj F))},{0}} is non empty set
<*S1,S2*> is Relation-like NAT -defined the carrier of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of C1
(Obj F) * <*S1,S2*> is Relation-like NAT -defined the carrier of C2 -valued Function-like Element of bool [:NAT, the carrier of C2:]
[:NAT, the carrier of C2:] is Relation-like non empty set
bool [:NAT, the carrier of C2:] is non empty set
[0,((Obj F) * <*S1,S2*>)] is V21() set
{0,((Obj F) * <*S1,S2*>)} is functional non empty set
{{0,((Obj F) * <*S1,S2*>)},{0}} is non empty set
<*((Obj F) . S1),((Obj F) . S2)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
[0,<*((Obj F) . S1),((Obj F) . S2)*>] is V21() set
{0,<*((Obj F) . S1),((Obj F) . S2)*>} is functional non empty set
{{0,<*((Obj F) . S1),((Obj F) . S2)*>},{0}} is non empty set
<*(F . S1),((Obj F) . S2)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
[0,<*(F . S1),((Obj F) . S2)*>] is V21() set
{0,<*(F . S1),((Obj F) . S2)*>} is functional non empty set
{{0,<*(F . S1),((Obj F) . S2)*>},{0}} is non empty set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
the carrier' of ( the carrier of C2) is non empty set
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
(C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
[: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is non empty set
S1 is Element of the carrier of C1
( the carrier of C1,S1) is Element of the carrier' of ( the carrier of C1)
<*S1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*S1*>] is V21() set
{1,<*S1*>} is non empty set
{{1,<*S1*>},{1}} is non empty set
(C1,C2,F) . ( the carrier of C1,S1) is Element of the carrier' of ( the carrier of C2)
F . S1 is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . S1 is Element of the carrier of C2
( the carrier of C2,(F . S1)) is Element of the carrier' of ( the carrier of C2)
<*(F . S1)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*(F . S1)*>] is V21() set
{1,<*(F . S1)*>} is non empty set
{{1,<*(F . S1)*>},{1}} is non empty set
dom (Obj F) is non empty Element of bool the carrier of C1
bool the carrier of C1 is non empty set
( the carrier of C1,S1) `1 is set
( the carrier of C1,S1) `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
<*S1*> is Relation-like NAT -defined the carrier of C1 -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of C1
(Obj F) * <*S1*> is Relation-like NAT -defined the carrier of C2 -valued Function-like Element of bool [:NAT, the carrier of C2:]
[:NAT, the carrier of C2:] is Relation-like non empty set
bool [:NAT, the carrier of C2:] is non empty set
[1,((Obj F) * <*S1*>)] is V21() set
{1,((Obj F) * <*S1*>)} is non empty set
{{1,((Obj F) * <*S1*>)},{1}} is non empty set
<*((Obj F) . S1)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
[1,<*((Obj F) . S1)*>] is V21() set
{1,<*((Obj F) . S1)*>} is non empty set
{{1,<*((Obj F) . S1)*>},{1}} is non empty set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
the carrier' of ( the carrier of C2) is non empty set
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
(C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
[: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is non empty set
S1 is Element of the carrier of C1
S2 is Element of the carrier of C1
A1 is Element of the carrier of C1
( the carrier of C1,S1,S2,A1) is Element of the carrier' of ( the carrier of C1)
<*S1,S2,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*S1,S2,A1*>] is V21() set
{2,<*S1,S2,A1*>} is non empty set
{{2,<*S1,S2,A1*>},{2}} is non empty set
(C1,C2,F) . ( the carrier of C1,S1,S2,A1) is Element of the carrier' of ( the carrier of C2)
F . S1 is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . S1 is Element of the carrier of C2
F . S2 is Element of the carrier of C2
(Obj F) . S2 is Element of the carrier of C2
F . A1 is Element of the carrier of C2
(Obj F) . A1 is Element of the carrier of C2
( the carrier of C2,(F . S1),(F . S2),(F . A1)) is Element of the carrier' of ( the carrier of C2)
<*(F . S1),(F . S2),(F . A1)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*(F . S1),(F . S2),(F . A1)*>] is V21() set
{2,<*(F . S1),(F . S2),(F . A1)*>} is non empty set
{{2,<*(F . S1),(F . S2),(F . A1)*>},{2}} is non empty set
dom (Obj F) is non empty Element of bool the carrier of C1
bool the carrier of C1 is non empty set
( the carrier of C1,S1,S2,A1) `1 is set
( the carrier of C1,S1,S2,A1) `2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
<*S1,S2,A1*> is Relation-like NAT -defined the carrier of C1 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of C1
(Obj F) * <*S1,S2,A1*> is Relation-like NAT -defined the carrier of C2 -valued Function-like Element of bool [:NAT, the carrier of C2:]
[:NAT, the carrier of C2:] is Relation-like non empty set
bool [:NAT, the carrier of C2:] is non empty set
[2,((Obj F) * <*S1,S2,A1*>)] is V21() set
{2,((Obj F) * <*S1,S2,A1*>)} is non empty set
{{2,((Obj F) * <*S1,S2,A1*>)},{2}} is non empty set
<*((Obj F) . S1),((Obj F) . S2),((Obj F) . A1)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
[2,<*((Obj F) . S1),((Obj F) . S2),((Obj F) . A1)*>] is V21() set
{2,<*((Obj F) . S1),((Obj F) . S2),((Obj F) . A1)*>} is non empty set
{{2,<*((Obj F) . S1),((Obj F) . S2),((Obj F) . A1)*>},{2}} is non empty set
<*(F . S1),((Obj F) . S2),((Obj F) . A1)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
[2,<*(F . S1),((Obj F) . S2),((Obj F) . A1)*>] is V21() set
{2,<*(F . S1),((Obj F) . S2),((Obj F) . A1)*>} is non empty set
{{2,<*(F . S1),((Obj F) . S2),((Obj F) . A1)*>},{2}} is non empty set
<*(F . S1),(F . S2),((Obj F) . A1)*> is Relation-like NAT -defined the carrier of C2 -valued Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of C2
[2,<*(F . S1),(F . S2),((Obj F) . A1)*>] is V21() set
{2,<*(F . S1),(F . S2),((Obj F) . A1)*>} is non empty set
{{2,<*(F . S1),(F . S2),((Obj F) . A1)*>},{2}} is non empty set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
(C1,C2,F) is Relation-like the carrier of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):]
the carrier of ( the carrier of C1) is non empty set
the carrier of ( the carrier of C2) is non empty set
[: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
(C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
the carrier' of ( the carrier of C1) is non empty set
the carrier' of ( the carrier of C2) is non empty set
[: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is non empty set
dom (C1,C2,F) is non empty Element of bool the carrier of ( the carrier of C1)
bool the carrier of ( the carrier of C1) is non empty set
dom (C1,C2,F) is non empty Element of bool the carrier' of ( the carrier of C1)
bool the carrier' of ( the carrier of C1) is non empty set
proj2 (C1,C2,F) is non empty set
proj2 (C1,C2,F) is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * (C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total set
the ResultSort of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C2) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):]
[: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):] is non empty set
(C1,C2,F) * the ResultSort of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C2) -defined the carrier of ( the carrier of C2) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):]
the carrier of ( the carrier of C2) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C2)
[: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is non empty set
rng (C1,C2,F) is non empty Element of bool the carrier of ( the carrier of C2)
bool the carrier of ( the carrier of C2) is non empty set
rng (C1,C2,F) is non empty Element of bool the carrier' of ( the carrier of C2)
bool the carrier' of ( the carrier of C2) is non empty set
f is Element of the carrier' of ( the carrier of C1)
f `1 is set
G is Element of the carrier of C1
( the carrier of C1,G) is Element of the carrier' of ( the carrier of C1)
<*G*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*G*>] is V21() set
{1,<*G*>} is non empty set
{{1,<*G*>},{1}} is non empty set
(C1,C2,F) * the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
((C1,C2,F) * the ResultSort of ( the carrier of C1)) . f is Element of the carrier of ( the carrier of C2)
the_result_sort_of f is Element of the carrier of ( the carrier of C1)
the ResultSort of ( the carrier of C1) . f is Element of the carrier of ( the carrier of C1)
(C1,C2,F) . (the_result_sort_of f) is Element of the carrier of ( the carrier of C2)
( the carrier of C1,G,G) is Element of the carrier of ( the carrier of C1)
<*G,G*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*G,G*>] is V21() set
{0,<*G,G*>} is functional non empty set
{{0,<*G,G*>},{0}} is non empty set
(C1,C2,F) . ( the carrier of C1,G,G) is Element of the carrier of ( the carrier of C2)
F . G is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . G is Element of the carrier of C2
( the carrier of C2,(F . G),(F . G)) is Element of the carrier of ( the carrier of C2)
<*(F . G),(F . G)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . G),(F . G)*>] is V21() set
{0,<*(F . G),(F . G)*>} is functional non empty set
{{0,<*(F . G),(F . G)*>},{0}} is non empty set
( the carrier of C2,(F . G)) is Element of the carrier' of ( the carrier of C2)
<*(F . G)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*(F . G)*>] is V21() set
{1,<*(F . G)*>} is non empty set
{{1,<*(F . G)*>},{1}} is non empty set
the_result_sort_of ( the carrier of C2,(F . G)) is Element of the carrier of ( the carrier of C2)
the ResultSort of ( the carrier of C2) . ( the carrier of C2,(F . G)) is Element of the carrier of ( the carrier of C2)
(C1,C2,F) . ( the carrier of C1,G) is Element of the carrier' of ( the carrier of C2)
the ResultSort of ( the carrier of C2) . ((C1,C2,F) . ( the carrier of C1,G)) is Element of the carrier of ( the carrier of C2)
the ResultSort of ( the carrier of C2) * (C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
( the ResultSort of ( the carrier of C2) * (C1,C2,F)) . f is Element of the carrier of ( the carrier of C2)
f is Element of the carrier' of ( the carrier of C1)
f `1 is set
G is Element of the carrier of C1
B1 is Element of the carrier of C1
H is Element of the carrier of C1
( the carrier of C1,G,B1,H) is Element of the carrier' of ( the carrier of C1)
<*G,B1,H*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*G,B1,H*>] is V21() set
{2,<*G,B1,H*>} is non empty set
{{2,<*G,B1,H*>},{2}} is non empty set
(C1,C2,F) * the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
((C1,C2,F) * the ResultSort of ( the carrier of C1)) . f is Element of the carrier of ( the carrier of C2)
the_result_sort_of f is Element of the carrier of ( the carrier of C1)
the ResultSort of ( the carrier of C1) . f is Element of the carrier of ( the carrier of C1)
(C1,C2,F) . (the_result_sort_of f) is Element of the carrier of ( the carrier of C2)
( the carrier of C1,G,H) is Element of the carrier of ( the carrier of C1)
<*G,H*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*G,H*>] is V21() set
{0,<*G,H*>} is functional non empty set
{{0,<*G,H*>},{0}} is non empty set
(C1,C2,F) . ( the carrier of C1,G,H) is Element of the carrier of ( the carrier of C2)
F . G is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . G is Element of the carrier of C2
F . H is Element of the carrier of C2
(Obj F) . H is Element of the carrier of C2
( the carrier of C2,(F . G),(F . H)) is Element of the carrier of ( the carrier of C2)
<*(F . G),(F . H)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . G),(F . H)*>] is V21() set
{0,<*(F . G),(F . H)*>} is functional non empty set
{{0,<*(F . G),(F . H)*>},{0}} is non empty set
F . B1 is Element of the carrier of C2
(Obj F) . B1 is Element of the carrier of C2
( the carrier of C2,(F . G),(F . B1),(F . H)) is Element of the carrier' of ( the carrier of C2)
<*(F . G),(F . B1),(F . H)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*(F . G),(F . B1),(F . H)*>] is V21() set
{2,<*(F . G),(F . B1),(F . H)*>} is non empty set
{{2,<*(F . G),(F . B1),(F . H)*>},{2}} is non empty set
the_result_sort_of ( the carrier of C2,(F . G),(F . B1),(F . H)) is Element of the carrier of ( the carrier of C2)
the ResultSort of ( the carrier of C2) . ( the carrier of C2,(F . G),(F . B1),(F . H)) is Element of the carrier of ( the carrier of C2)
(C1,C2,F) . ( the carrier of C1,G,B1,H) is Element of the carrier' of ( the carrier of C2)
the ResultSort of ( the carrier of C2) . ((C1,C2,F) . ( the carrier of C1,G,B1,H)) is Element of the carrier of ( the carrier of C2)
the ResultSort of ( the carrier of C2) * (C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
( the ResultSort of ( the carrier of C2) * (C1,C2,F)) . f is Element of the carrier of ( the carrier of C2)
f is Element of the carrier' of ( the carrier of C1)
f `1 is set
(C1,C2,F) * the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
the ResultSort of ( the carrier of C2) * (C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
(C1,C2,F) * the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
the ResultSort of ( the carrier of C2) * (C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C2):]
f is set
the Arity of ( the carrier of C1) . f is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
(C1,C2,F) . f is set
the Arity of ( the carrier of C2) . ((C1,C2,F) . f) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like set
G is Relation-like Function-like set
G * (C1,C2,F) is Relation-like the carrier of ( the carrier of C2) -valued Function-like set
B1 is Element of the carrier' of ( the carrier of C1)
B1 `1 is set
H is Element of the carrier of C1
( the carrier of C1,H) is Element of the carrier' of ( the carrier of C1)
<*H*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*H*>] is V21() set
{1,<*H*>} is non empty set
{{1,<*H*>},{1}} is non empty set
{} * (C1,C2,F) is Relation-like non-empty empty-yielding NAT -defined the carrier of ( the carrier of C2) -valued V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() set
F . H is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . H is Element of the carrier of C2
( the carrier of C2,(F . H)) is Element of the carrier' of ( the carrier of C2)
<*(F . H)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*(F . H)*>] is V21() set
{1,<*(F . H)*>} is non empty set
{{1,<*(F . H)*>},{1}} is non empty set
the_arity_of ( the carrier of C2,(F . H)) is Relation-like NAT -defined the carrier of ( the carrier of C2) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C2) *
the Arity of ( the carrier of C2) . ( the carrier of C2,(F . H)) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C2) *
B1 is Element of the carrier' of ( the carrier of C1)
B1 `1 is set
H is Element of the carrier of C1
o is Element of the carrier of C1
x is Element of the carrier of C1
( the carrier of C1,H,o,x) is Element of the carrier' of ( the carrier of C1)
<*H,o,x*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*H,o,x*>] is V21() set
{2,<*H,o,x*>} is non empty set
{{2,<*H,o,x*>},{2}} is non empty set
( the carrier of C1,o,x) is Element of the carrier of ( the carrier of C1)
<*o,x*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*o,x*>] is V21() set
{0,<*o,x*>} is functional non empty set
{{0,<*o,x*>},{0}} is non empty set
( the carrier of C1,H,o) is Element of the carrier of ( the carrier of C1)
<*H,o*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*H,o*>] is V21() set
{0,<*H,o*>} is functional non empty set
{{0,<*H,o*>},{0}} is non empty set
<*( the carrier of C1,o,x),( the carrier of C1,H,o)*> is Relation-like NAT -defined the carrier of ( the carrier of C1) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of C1)
(C1,C2,F) . ( the carrier of C1,o,x) is Element of the carrier of ( the carrier of C2)
(C1,C2,F) . ( the carrier of C1,H,o) is Element of the carrier of ( the carrier of C2)
<*((C1,C2,F) . ( the carrier of C1,o,x)),((C1,C2,F) . ( the carrier of C1,H,o))*> is Relation-like NAT -defined the carrier of ( the carrier of C2) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of C2)
F . o is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . o is Element of the carrier of C2
F . x is Element of the carrier of C2
(Obj F) . x is Element of the carrier of C2
( the carrier of C2,(F . o),(F . x)) is Element of the carrier of ( the carrier of C2)
<*(F . o),(F . x)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . o),(F . x)*>] is V21() set
{0,<*(F . o),(F . x)*>} is functional non empty set
{{0,<*(F . o),(F . x)*>},{0}} is non empty set
<*( the carrier of C2,(F . o),(F . x)),((C1,C2,F) . ( the carrier of C1,H,o))*> is Relation-like NAT -defined the carrier of ( the carrier of C2) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of C2)
F . H is Element of the carrier of C2
(Obj F) . H is Element of the carrier of C2
( the carrier of C2,(F . H),(F . o)) is Element of the carrier of ( the carrier of C2)
<*(F . H),(F . o)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . H),(F . o)*>] is V21() set
{0,<*(F . H),(F . o)*>} is functional non empty set
{{0,<*(F . H),(F . o)*>},{0}} is non empty set
<*( the carrier of C2,(F . o),(F . x)),( the carrier of C2,(F . H),(F . o))*> is Relation-like NAT -defined the carrier of ( the carrier of C2) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of C2)
( the carrier of C2,(F . H),(F . o),(F . x)) is Element of the carrier' of ( the carrier of C2)
<*(F . H),(F . o),(F . x)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*(F . H),(F . o),(F . x)*>] is V21() set
{2,<*(F . H),(F . o),(F . x)*>} is non empty set
{{2,<*(F . H),(F . o),(F . x)*>},{2}} is non empty set
the_arity_of ( the carrier of C2,(F . H),(F . o),(F . x)) is Relation-like NAT -defined the carrier of ( the carrier of C2) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C2) *
the Arity of ( the carrier of C2) . ( the carrier of C2,(F . H),(F . o),(F . x)) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C2) *
B1 is Element of the carrier' of ( the carrier of C1)
B1 `1 is set
C1 is non empty set
(C1) is non empty non void feasible strict feasible () () (C1)
C2 is MSAlgebra over (C1)
F is Element of C1
(C1,F) is Element of the carrier' of (C1)
the carrier' of (C1) is non empty set
<*F*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*F*>] is V21() set
{1,<*F*>} is non empty set
{{1,<*F*>},{1}} is non empty set
Args ((C1,F),C2) is Element of proj2 ( the Sorts of C2 #)
the carrier of (C1) is non empty set
the Sorts of C2 is Relation-like the carrier of (C1) -defined Function-like non empty total set
the Sorts of C2 # is Relation-like the carrier of (C1) * -defined Function-like non empty total set
the carrier of (C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of (C1)
proj2 ( the Sorts of C2 #) is non empty set
the Arity of (C1) is Relation-like the carrier' of (C1) -defined the carrier of (C1) * -valued Function-like non empty total V36( the carrier' of (C1), the carrier of (C1) * ) Function-yielding V78() Element of bool [: the carrier' of (C1),( the carrier of (C1) *):]
[: the carrier' of (C1),( the carrier of (C1) *):] is Relation-like non empty set
bool [: the carrier' of (C1),( the carrier of (C1) *):] is non empty set
the Arity of (C1) * ( the Sorts of C2 #) is Relation-like the carrier' of (C1) -defined Function-like non empty total set
( the Arity of (C1) * ( the Sorts of C2 #)) . (C1,F) is set
the_arity_of (C1,F) is Relation-like NAT -defined the carrier of (C1) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (C1) *
the Arity of (C1) . (C1,F) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (C1) *
(the_arity_of (C1,F)) * the Sorts of C2 is Relation-like NAT -defined Function-like set
product ((the_arity_of (C1,F)) * the Sorts of C2) is set
{} * the Sorts of C2 is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() set
product ({} * the Sorts of C2) is set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier' of C1 is non empty set
bool the carrier' of C1 is non empty set
C2 is MSAlgebra over ( the carrier of C1)
the Sorts of C2 is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
the carrier of ( the carrier of C1) is non empty set
F is Element of the carrier of C1
S1 is Element of the carrier of C1
S2 is Element of the carrier of C1
( the carrier of C1,F,S1,S2) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*F,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*F,S1,S2*>] is V21() set
{2,<*F,S1,S2*>} is non empty set
{{2,<*F,S1,S2*>},{2}} is non empty set
Args (( the carrier of C1,F,S1,S2),C2) is Element of proj2 ( the Sorts of C2 #)
the Sorts of C2 # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of C2 #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of C2 #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of C2 #)) . ( the carrier of C1,F,S1,S2) is set
Hom (S1,S2) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = S1 & cod b₁ = S2 ) } is set
Hom (F,S1) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = S1 ) } is set
<*(Hom (S1,S2)),(Hom (F,S1))*> is Relation-like NAT -defined bool the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of bool the carrier' of C1
product <*(Hom (S1,S2)),(Hom (F,S1))*> is set
Result (( the carrier of C1,F,S1,S2),C2) is Element of proj2 the Sorts of C2
proj2 the Sorts of C2 is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of C2) . ( the carrier of C1,F,S1,S2) is set
Hom (F,S2) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = S2 ) } is set
dom the Sorts of C2 is non empty Element of bool the carrier of ( the carrier of C1)
bool the carrier of ( the carrier of C1) is non empty set
the_arity_of ( the carrier of C1,F,S1,S2) is Relation-like NAT -defined the carrier of ( the carrier of C1) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C1) *
the Arity of ( the carrier of C1) . ( the carrier of C1,F,S1,S2) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C1) *
(the_arity_of ( the carrier of C1,F,S1,S2)) * the Sorts of C2 is Relation-like NAT -defined Function-like set
product ((the_arity_of ( the carrier of C1,F,S1,S2)) * the Sorts of C2) is set
( the carrier of C1,S1,S2) is Element of the carrier of ( the carrier of C1)
<*S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S1,S2*>] is V21() set
{0,<*S1,S2*>} is functional non empty set
{{0,<*S1,S2*>},{0}} is non empty set
( the carrier of C1,F,S1) is Element of the carrier of ( the carrier of C1)
<*F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*F,S1*>] is V21() set
{0,<*F,S1*>} is functional non empty set
{{0,<*F,S1*>},{0}} is non empty set
<*( the carrier of C1,S1,S2),( the carrier of C1,F,S1)*> is Relation-like NAT -defined the carrier of ( the carrier of C1) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of C1)
<*( the carrier of C1,S1,S2),( the carrier of C1,F,S1)*> * the Sorts of C2 is Relation-like NAT -defined Function-like set
product (<*( the carrier of C1,S1,S2),( the carrier of C1,F,S1)*> * the Sorts of C2) is set
the Sorts of C2 . ( the carrier of C1,S1,S2) is set
the Sorts of C2 . ( the carrier of C1,F,S1) is set
<*( the Sorts of C2 . ( the carrier of C1,S1,S2)),( the Sorts of C2 . ( the carrier of C1,F,S1))*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
product <*( the Sorts of C2 . ( the carrier of C1,S1,S2)),( the Sorts of C2 . ( the carrier of C1,F,S1))*> is set
<*(Hom (S1,S2)),( the Sorts of C2 . ( the carrier of C1,F,S1))*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
product <*(Hom (S1,S2)),( the Sorts of C2 . ( the carrier of C1,F,S1))*> is set
the_result_sort_of ( the carrier of C1,F,S1,S2) is Element of the carrier of ( the carrier of C1)
the ResultSort of ( the carrier of C1) . ( the carrier of C1,F,S1,S2) is Element of the carrier of ( the carrier of C1)
the Sorts of C2 . (the_result_sort_of ( the carrier of C1,F,S1,S2)) is set
( the carrier of C1,F,S2) is Element of the carrier of ( the carrier of C1)
<*F,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*F,S2*>] is V21() set
{0,<*F,S2*>} is functional non empty set
{{0,<*F,S2*>},{0}} is non empty set
the Sorts of C2 . ( the carrier of C1,F,S2) is set
F₁() is non empty set
F₂() is non empty set
(F₁()) is non empty non void feasible strict feasible () () (F₁())
the carrier' of (F₁()) is non empty set
C2 is set
C2 `1 is set
F is Element of F<sub>1</sub>()
(F<sub>1</sub>(),F) is Element of the carrier' of (F<sub>1</sub>())
<*F*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*F*>] is V21() set
{1,<*F*>} is non empty set
{{1,<*F*>},{1}} is non empty set
F<sub>5</sub>(F) is set
{} :-> F<sub>5</sub>(F) is Relation-like {{}} -defined {F<sub>5</sub>(F)} -valued Function-like one-to-one non empty total V36({{}},{F<sub>5</sub>(F)}) Element of bool [:{{}},{F<sub>5</sub>(F)}:]
{F<sub>5</sub>(F)} is non empty set
[:{{}},{F<sub>5</sub>(F)}:] is Relation-like non empty set
bool [:{{}},{F<sub>5</sub>(F)}:] is non empty set
{{}} --> F<sub>5</sub>(F) is Relation-like {{}} -defined {F<sub>5</sub>(F)} -valued Function-like constant non empty total V36({{}},{F<sub>5</sub>(F)}) Element of bool [:{{}},{F<sub>5</sub>(F)}:]
S2 is set
A2 is Element of F<sub>1</sub>()
(F<sub>1</sub>(),A2) is Element of the carrier' of (F<sub>1</sub>())
<*A2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*A2*>] is V21() set
{1,<*A2*>} is non empty set
{{1,<*A2*>},{1}} is non empty set
F<sub>5</sub>(A2) is set
F<sub>3</sub>(A2,A2) is set
{F<sub>5</sub>(A2)} is non empty set
dom ({} :-> F<sub>5</sub>(F)) is functional non empty Element of bool {{}}
bool {{}} is non empty set
rng ({} :-> F<sub>5</sub>(F)) is non empty Element of bool {F<sub>5</sub>(F)}
bool {F<sub>5</sub>(F)} is non empty set
[:{{}},F<sub>3</sub>(A2,A2):] is Relation-like set
bool [:{{}},F<sub>3</sub>(A2,A2):] is non empty set
f is Relation-like {{}} -defined F<sub>3</sub>(A2,A2) -valued Function-like V36({{}},F<sub>3</sub>(A2,A2)) Element of bool [:{{}},F<sub>3</sub>(A2,A2):]
G is Relation-like {{}} -defined F<sub>3</sub>(A2,A2) -valued Function-like V36({{}},F<sub>3</sub>(A2,A2)) Element of bool [:{{}},F<sub>3</sub>(A2,A2):]
A1 is set
G . {} is set
F is Element of F<sub>1</sub>()
S1 is Element of F<sub>1</sub>()
S2 is Element of F<sub>1</sub>()
(F<sub>1</sub>(),F,S1,S2) is Element of the carrier' of (F<sub>1</sub>())
<*F,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*F,S1,S2*>] is V21() set
{2,<*F,S1,S2*>} is non empty set
{{2,<*F,S1,S2*>},{2}} is non empty set
F<sub>3</sub>(F,S1) is set
F<sub>3</sub>(S1,S2) is set
A1 is set
<*F<sub>3</sub>(S1,S2),F<sub>3</sub>(F,S1)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
product <*F<sub>3</sub>(S1,S2),F<sub>3</sub>(F,S1)*> is set
A2 is set
f is set
<*A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
F<sub>4</sub>(F,S1,S2,A2,f) is set
G is set
F<sub>3</sub>(F,S2) is set
A1 is Relation-like Function-like set
proj1 A1 is set
proj2 A1 is set
A2 is set
G is Element of F<sub>1</sub>()
B1 is Element of F<sub>1</sub>()
H is Element of F<sub>1</sub>()
(F<sub>1</sub>(),G,B1,H) is Element of the carrier' of (F<sub>1</sub>())
<*G,B1,H*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*G,B1,H*>] is V21() set
{2,<*G,B1,H*>} is non empty set
{{2,<*G,B1,H*>},{2}} is non empty set
F<sub>3</sub>(B1,H) is set
F<sub>3</sub>(G,B1) is set
<*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*> is set
F<sub>3</sub>(G,H) is set
[:(product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*>),F<sub>3</sub>(G,H):] is Relation-like set
bool [:(product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*>),F<sub>3</sub>(G,H):] is non empty set
o is Relation-like product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*> -defined F<sub>3</sub>(G,H) -valued Function-like V36( product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*>,F<sub>3</sub>(G,H)) Element of bool [:(product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*>),F<sub>3</sub>(G,H):]
x is Relation-like product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*> -defined F<sub>3</sub>(G,H) -valued Function-like V36( product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*>,F<sub>3</sub>(G,H)) Element of bool [:(product <*F<sub>3</sub>(B1,H),F<sub>3</sub>(G,B1)*>),F<sub>3</sub>(G,H):]
f is set
a is set
b is set
<*b,a*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
x . <*b,a*> is set
c is set
g is set
<*g,c*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
F<sub>4</sub>(G,B1,H,g,c) is set
<*b,a*> . 1 is set
<*b,a*> . 2 is set
F<sub>4</sub>(G,B1,H,b,a) is set
S1 is Element of F<sub>1</sub>()
F<sub>3</sub>(S1,S1) is set
[:{{}},F<sub>3</sub>(S1,S1):] is Relation-like set
bool [:{{}},F<sub>3</sub>(S1,S1):] is non empty set
f is Element of F<sub>1</sub>()
G is Element of F<sub>1</sub>()
F<sub>3</sub>(f,G) is set
A2 is Element of F<sub>1</sub>()
F<sub>3</sub>(A2,f) is set
<*F<sub>3</sub>(f,G),F<sub>3</sub>(A2,f)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
product <*F<sub>3</sub>(f,G),F<sub>3</sub>(A2,f)*> is set
F<sub>3</sub>(A2,G) is set
[:(product <*F<sub>3</sub>(f,G),F<sub>3</sub>(A2,f)*>),F<sub>3</sub>(A2,G):] is Relation-like set
bool [:(product <*F<sub>3</sub>(f,G),F<sub>3</sub>(A2,f)*>),F<sub>3</sub>(A2,G):] is non empty set
(F<sub>1</sub>(),S1) is Element of the carrier' of (F<sub>1</sub>())
<*S1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*S1*>] is V21() set
{1,<*S1*>} is non empty set
{{1,<*S1*>},{1}} is non empty set
S2 is Relation-like {{}} -defined F<sub>3</sub>(S1,S1) -valued Function-like V36({{}},F<sub>3</sub>(S1,S1)) Element of bool [:{{}},F<sub>3</sub>(S1,S1):]
F is set
S2 . {} is set
F<sub>5</sub>(S1) is set
(F<sub>1</sub>(),A2,f,G) is Element of the carrier' of (F<sub>1</sub>())
<*A2,f,G*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*A2,f,G*>] is V21() set
{2,<*A2,f,G*>} is non empty set
{{2,<*A2,f,G*>},{2}} is non empty set
B1 is Relation-like product <*F<sub>3</sub>(f,G),F<sub>3</sub>(A2,f)*> -defined F<sub>3</sub>(A2,G) -valued Function-like V36( product <*F<sub>3</sub>(f,G),F<sub>3</sub>(A2,f)*>,F<sub>3</sub>(A2,G)) Element of bool [:(product <*F<sub>3</sub>(f,G),F<sub>3</sub>(A2,f)*>),F<sub>3</sub>(A2,G):]
A1 is set
C2 is Relation-like Function-like set
proj1 C2 is set
S1 is set
the carrier of (F<sub>1</sub>()) is non empty set
S2 is Element of F<sub>1</sub>()
A1 is Element of F<sub>1</sub>()
(F<sub>1</sub>(),S2,A1) is Element of the carrier of (F<sub>1</sub>())
<*S2,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,A1*>] is V21() set
{0,<*S2,A1*>} is functional non empty set
{{0,<*S2,A1*>},{0}} is non empty set
F<sub>3</sub>(S2,A1) is set
A2 is set
S1 is Relation-like Function-like set
proj1 S1 is set
F is Relation-like the carrier' of (F<sub>1</sub>()) -defined Function-like non empty total set
the Arity of (F<sub>1</sub>()) is Relation-like the carrier' of (F<sub>1</sub>()) -defined the carrier of (F<sub>1</sub>()) * -valued Function-like non empty total V36( the carrier' of (F<sub>1</sub>()), the carrier of (F<sub>1</sub>()) * ) Function-yielding V78() Element of bool [: the carrier' of (F<sub>1</sub>()),( the carrier of (F<sub>1</sub>()) *):]
the carrier of (F<sub>1</sub>()) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of (F<sub>1</sub>())
[: the carrier' of (F<sub>1</sub>()),( the carrier of (F<sub>1</sub>()) *):] is Relation-like non empty set
bool [: the carrier' of (F<sub>1</sub>()),( the carrier of (F<sub>1</sub>()) *):] is non empty set
S2 is Relation-like the carrier of (F<sub>1</sub>()) -defined Function-like non empty total set
S2 # is Relation-like the carrier of (F<sub>1</sub>()) * -defined Function-like non empty total set
the Arity of (F<sub>1</sub>()) * (S2 #) is Relation-like the carrier' of (F<sub>1</sub>()) -defined Function-like non empty total set
the ResultSort of (F<sub>1</sub>()) is Relation-like the carrier' of (F<sub>1</sub>()) -defined the carrier of (F<sub>1</sub>()) -valued Function-like non empty total V36( the carrier' of (F<sub>1</sub>()), the carrier of (F<sub>1</sub>())) Element of bool [: the carrier' of (F<sub>1</sub>()), the carrier of (F<sub>1</sub>()):]
[: the carrier' of (F<sub>1</sub>()), the carrier of (F<sub>1</sub>()):] is Relation-like non empty set
bool [: the carrier' of (F<sub>1</sub>()), the carrier of (F<sub>1</sub>()):] is non empty set
the ResultSort of (F<sub>1</sub>()) * S2 is Relation-like the carrier' of (F<sub>1</sub>()) -defined Function-like non empty total set
A1 is set
F . A1 is set
( the Arity of (F<sub>1</sub>()) * (S2 #)) . A1 is set
( the ResultSort of (F<sub>1</sub>()) * S2) . A1 is set
[:(( the Arity of (F<sub>1</sub>()) * (S2 #)) . A1),(( the ResultSort of (F<sub>1</sub>()) * S2) . A1):] is Relation-like set
bool [:(( the Arity of (F<sub>1</sub>()) * (S2 #)) . A1),(( the ResultSort of (F<sub>1</sub>()) * S2) . A1):] is non empty set
A2 is Element of the carrier' of (F<sub>1</sub>())
( the Arity of (F<sub>1</sub>()) * (S2 #)) . A2 is set
the_arity_of A2 is Relation-like NAT -defined the carrier of (F<sub>1</sub>()) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (F<sub>1</sub>()) *
the Arity of (F<sub>1</sub>()) . A2 is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (F<sub>1</sub>()) *
(S2 #) . (the_arity_of A2) is set
(the_arity_of A2) * S2 is Relation-like NAT -defined Function-like set
product ((the_arity_of A2) * S2) is set
( the ResultSort of (F<sub>1</sub>()) * S2) . A2 is set
the_result_sort_of A2 is Element of the carrier of (F<sub>1</sub>())
the ResultSort of (F<sub>1</sub>()) . A2 is Element of the carrier of (F<sub>1</sub>())
S2 . (the_result_sort_of A2) is set
A2 `1 is set
F . A2 is set
f is Element of F₁()
(F₁(),f) is Element of the carrier' of (F₁())
<*f*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*f*>] is V21() set
{1,<*f*>} is non empty set
{{1,<*f*>},{1}} is non empty set
F₃(f,f) is set
[:{{}},F₃(f,f):] is Relation-like set
bool [:{{}},F₃(f,f):] is non empty set
F₅(f) is set
the_arity_of (F₁(),f) is Relation-like NAT -defined the carrier of (F₁()) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (F₁()) *
the Arity of (F₁()) . (F₁(),f) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (F₁()) *
{} * S2 is Relation-like non-empty empty-yielding NAT -defined V6() V7() V8() V10() V11() V12() Function-like one-to-one constant functional empty V24() FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V78() set
the_result_sort_of (F₁(),f) is Element of the carrier of (F₁())
the ResultSort of (F₁()) . (F₁(),f) is Element of the carrier of (F₁())
(F₁(),f,f) is Element of the carrier of (F₁())
<*f,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*f,f*>] is V21() set
{0,<*f,f*>} is functional non empty set
{{0,<*f,f*>},{0}} is non empty set
S2 . (F₁(),f,f) is set
G is Element of F₁()
B1 is Element of F₁()
(F₁(),G,B1) is Element of the carrier of (F₁())
<*G,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*G,B1*>] is V21() set
{0,<*G,B1*>} is functional non empty set
{{0,<*G,B1*>},{0}} is non empty set
F₃(G,B1) is set
H is Relation-like {{}} -defined F₃(f,f) -valued Function-like V36({{}},F₃(f,f)) Element of bool [:{{}},F₃(f,f):]
H . {} is set
A2 `1 is set
F . A2 is set
f is Element of F<sub>1</sub>()
G is Element of F<sub>1</sub>()
B1 is Element of F<sub>1</sub>()
(F<sub>1</sub>(),f,G,B1) is Element of the carrier' of (F<sub>1</sub>())
<*f,G,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*f,G,B1*>] is V21() set
{2,<*f,G,B1*>} is non empty set
{{2,<*f,G,B1*>},{2}} is non empty set
F<sub>3</sub>(G,B1) is set
F<sub>3</sub>(f,G) is set
<*F<sub>3</sub>(G,B1),F<sub>3</sub>(f,G)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
product <*F<sub>3</sub>(G,B1),F<sub>3</sub>(f,G)*> is set
F<sub>3</sub>(f,B1) is set
[:(product <*F<sub>3</sub>(G,B1),F<sub>3</sub>(f,G)*>),F<sub>3</sub>(f,B1):] is Relation-like set
bool [:(product <*F<sub>3</sub>(G,B1),F<sub>3</sub>(f,G)*>),F<sub>3</sub>(f,B1):] is non empty set
the_result_sort_of (F<sub>1</sub>(),f,G,B1) is Element of the carrier of (F<sub>1</sub>())
the ResultSort of (F<sub>1</sub>()) . (F<sub>1</sub>(),f,G,B1) is Element of the carrier of (F<sub>1</sub>())
(F<sub>1</sub>(),f,B1) is Element of the carrier of (F<sub>1</sub>())
<*f,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*f,B1*>] is V21() set
{0,<*f,B1*>} is functional non empty set
{{0,<*f,B1*>},{0}} is non empty set
S2 . (F<sub>1</sub>(),f,B1) is set
H is Element of F<sub>1</sub>()
o is Element of F<sub>1</sub>()
(F<sub>1</sub>(),H,o) is Element of the carrier of (F<sub>1</sub>())
<*H,o*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*H,o*>] is V21() set
{0,<*H,o*>} is functional non empty set
{{0,<*H,o*>},{0}} is non empty set
F<sub>3</sub>(H,o) is set
the_arity_of (F<sub>1</sub>(),f,G,B1) is Relation-like NAT -defined the carrier of (F<sub>1</sub>()) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (F<sub>1</sub>()) *
the Arity of (F<sub>1</sub>()) . (F<sub>1</sub>(),f,G,B1) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of (F<sub>1</sub>()) *
(F<sub>1</sub>(),G,B1) is Element of the carrier of (F<sub>1</sub>())
<*G,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*G,B1*>] is V21() set
{0,<*G,B1*>} is functional non empty set
{{0,<*G,B1*>},{0}} is non empty set
(F<sub>1</sub>(),f,G) is Element of the carrier of (F<sub>1</sub>())
<*f,G*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*f,G*>] is V21() set
{0,<*f,G*>} is functional non empty set
{{0,<*f,G*>},{0}} is non empty set
<*(F<sub>1</sub>(),G,B1),(F<sub>1</sub>(),f,G)*> is Relation-like NAT -defined the carrier of (F<sub>1</sub>()) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (F<sub>1</sub>())
S2 . (F<sub>1</sub>(),f,G) is set
x is Element of F<sub>1</sub>()
a is Element of F<sub>1</sub>()
(F<sub>1</sub>(),x,a) is Element of the carrier of (F<sub>1</sub>())
<*x,a*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*x,a*>] is V21() set
{0,<*x,a*>} is functional non empty set
{{0,<*x,a*>},{0}} is non empty set
F<sub>3</sub>(x,a) is set
S2 . (F<sub>1</sub>(),G,B1) is set
b is Element of F<sub>1</sub>()
c is Element of F<sub>1</sub>()
(F<sub>1</sub>(),b,c) is Element of the carrier of (F<sub>1</sub>())
<*b,c*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*b,c*>] is V21() set
{0,<*b,c*>} is functional non empty set
{{0,<*b,c*>},{0}} is non empty set
F<sub>3</sub>(b,c) is set
g is Relation-like product <*F<sub>3</sub>(G,B1),F<sub>3</sub>(f,G)*> -defined F<sub>3</sub>(f,B1) -valued Function-like V36( product <*F<sub>3</sub>(G,B1),F<sub>3</sub>(f,G)*>,F<sub>3</sub>(f,B1)) Element of bool [:(product <*F<sub>3</sub>(G,B1),F<sub>3</sub>(f,G)*>),F<sub>3</sub>(f,B1):]
A2 `1 is set
A1 is Relation-like the carrier' of (F₁()) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of (F₁()) * (S2 #), the ResultSort of (F₁()) * S2
MSAlgebra(# S2,A1 #) is strict MSAlgebra over (F₁())
A2 is strict MSAlgebra over (F₁())
the Sorts of A2 is Relation-like the carrier of (F₁()) -defined Function-like non empty total set
f is Element of F₁()
G is Element of F₁()
(F₁(),f,G) is Element of the carrier of (F₁())
<*f,G*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*f,G*>] is V21() set
{0,<*f,G*>} is functional non empty set
{{0,<*f,G*>},{0}} is non empty set
S2 . (F₁(),f,G) is set
B1 is Element of F₁()
H is Element of F₁()
(F₁(),B1,H) is Element of the carrier of (F₁())
<*B1,H*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*B1,H*>] is V21() set
{0,<*B1,H*>} is functional non empty set
{{0,<*B1,H*>},{0}} is non empty set
F₃(B1,H) is set
the Sorts of A2 . (F₁(),f,G) is set
F₃(f,G) is set
f is Element of F₁()
(F₁(),f) is Element of the carrier' of (F₁())
<*f*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*f*>] is V21() set
{1,<*f*>} is non empty set
{{1,<*f*>},{1}} is non empty set
(F₁(),f) `1 is set
A1 . (F<sub>1</sub>(),f) is Relation-like ( the Arity of (F<sub>1</sub>()) * (S2 #)) . (F<sub>1</sub>(),f) -defined ( the ResultSort of (F<sub>1</sub>()) * S2) . (F<sub>1</sub>(),f) -valued Function-like V36(( the Arity of (F<sub>1</sub>()) * (S2 #)) . (F<sub>1</sub>(),f),( the ResultSort of (F<sub>1</sub>()) * S2) . (F<sub>1</sub>(),f)) Element of bool [:(( the Arity of (F<sub>1</sub>()) * (S2 #)) . (F<sub>1</sub>(),f)),(( the ResultSort of (F<sub>1</sub>()) * S2) . (F<sub>1</sub>(),f)):]
( the Arity of (F<sub>1</sub>()) * (S2 #)) . (F<sub>1</sub>(),f) is set
( the ResultSort of (F<sub>1</sub>()) * S2) . (F<sub>1</sub>(),f) is set
[:(( the Arity of (F<sub>1</sub>()) * (S2 #)) . (F<sub>1</sub>(),f)),(( the ResultSort of (F<sub>1</sub>()) * S2) . (F<sub>1</sub>(),f)):] is Relation-like set
bool [:(( the Arity of (F<sub>1</sub>()) * (S2 #)) . (F<sub>1</sub>(),f)),(( the ResultSort of (F<sub>1</sub>()) * S2) . (F<sub>1</sub>(),f)):] is non empty set
Den ((F<sub>1</sub>(),f),A2) is Relation-like Args ((F<sub>1</sub>(),f),A2) -defined Result ((F<sub>1</sub>(),f),A2) -valued Function-like V36( Args ((F<sub>1</sub>(),f),A2), Result ((F<sub>1</sub>(),f),A2)) Element of bool [:(Args ((F<sub>1</sub>(),f),A2)),(Result ((F<sub>1</sub>(),f),A2)):]
Args ((F<sub>1</sub>(),f),A2) is Element of proj2 ( the Sorts of A2 #)
the Sorts of A2 # is Relation-like the carrier of (F<sub>1</sub>()) * -defined Function-like non empty total set
proj2 ( the Sorts of A2 #) is non empty set
the Arity of (F<sub>1</sub>()) * ( the Sorts of A2 #) is Relation-like the carrier' of (F<sub>1</sub>()) -defined Function-like non empty total set
( the Arity of (F<sub>1</sub>()) * ( the Sorts of A2 #)) . (F<sub>1</sub>(),f) is set
Result ((F<sub>1</sub>(),f),A2) is Element of proj2 the Sorts of A2
proj2 the Sorts of A2 is non empty set
the ResultSort of (F<sub>1</sub>()) * the Sorts of A2 is Relation-like the carrier' of (F<sub>1</sub>()) -defined Function-like non empty total set
( the ResultSort of (F<sub>1</sub>()) * the Sorts of A2) . (F<sub>1</sub>(),f) is set
[:(Args ((F<sub>1</sub>(),f),A2)),(Result ((F<sub>1</sub>(),f),A2)):] is Relation-like set
bool [:(Args ((F<sub>1</sub>(),f),A2)),(Result ((F<sub>1</sub>(),f),A2)):] is non empty set
the Charact of A2 is Relation-like the carrier' of (F<sub>1</sub>()) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of (F<sub>1</sub>()) * ( the Sorts of A2 #), the ResultSort of (F<sub>1</sub>()) * the Sorts of A2
the Charact of A2 . (F<sub>1</sub>(),f) is Relation-like Function-like set
(Den ((F<sub>1</sub>(),f),A2)) . {} is set
F<sub>5</sub>(f) is set
G is Element of F<sub>1</sub>()
F<sub>3</sub>(G,G) is set
[:{{}},F<sub>3</sub>(G,G):] is Relation-like set
bool [:{{}},F<sub>3</sub>(G,G):] is non empty set
(F<sub>1</sub>(),G) is Element of the carrier' of (F<sub>1</sub>())
<*G*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*G*>] is V21() set
{1,<*G*>} is non empty set
{{1,<*G*>},{1}} is non empty set
B1 is Relation-like {{}} -defined F<sub>3</sub>(G,G) -valued Function-like V36({{}},F<sub>3</sub>(G,G)) Element of bool [:{{}},F<sub>3</sub>(G,G):]
B1 . {} is set
F<sub>5</sub>(G) is set
f is Element of F<sub>1</sub>()
G is Element of F<sub>1</sub>()
F<sub>3</sub>(f,G) is set
B1 is Element of F<sub>1</sub>()
F<sub>3</sub>(G,B1) is set
(F<sub>1</sub>(),f,G,B1) is Element of the carrier' of (F<sub>1</sub>())
<*f,G,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*f,G,B1*>] is V21() set
{2,<*f,G,B1*>} is non empty set
{{2,<*f,G,B1*>},{2}} is non empty set
Den ((F<sub>1</sub>(),f,G,B1),A2) is Relation-like Args ((F<sub>1</sub>(),f,G,B1),A2) -defined Result ((F<sub>1</sub>(),f,G,B1),A2) -valued Function-like V36( Args ((F<sub>1</sub>(),f,G,B1),A2), Result ((F<sub>1</sub>(),f,G,B1),A2)) Element of bool [:(Args ((F<sub>1</sub>(),f,G,B1),A2)),(Result ((F<sub>1</sub>(),f,G,B1),A2)):]
Args ((F<sub>1</sub>(),f,G,B1),A2) is Element of proj2 ( the Sorts of A2 #)
( the Arity of (F<sub>1</sub>()) * ( the Sorts of A2 #)) . (F<sub>1</sub>(),f,G,B1) is set
Result ((F<sub>1</sub>(),f,G,B1),A2) is Element of proj2 the Sorts of A2
( the ResultSort of (F<sub>1</sub>()) * the Sorts of A2) . (F<sub>1</sub>(),f,G,B1) is set
[:(Args ((F<sub>1</sub>(),f,G,B1),A2)),(Result ((F<sub>1</sub>(),f,G,B1),A2)):] is Relation-like set
bool [:(Args ((F<sub>1</sub>(),f,G,B1),A2)),(Result ((F<sub>1</sub>(),f,G,B1),A2)):] is non empty set
the Charact of A2 . (F<sub>1</sub>(),f,G,B1) is Relation-like Function-like set
(F<sub>1</sub>(),f,G,B1) `1 is set
A1 . (F₁(),f,G,B1) is Relation-like ( the Arity of (F₁()) * (S2 #)) . (F₁(),f,G,B1) -defined ( the ResultSort of (F₁()) * S2) . (F₁(),f,G,B1) -valued Function-like V36(( the Arity of (F₁()) * (S2 #)) . (F₁(),f,G,B1),( the ResultSort of (F₁()) * S2) . (F₁(),f,G,B1)) Element of bool [:(( the Arity of (F₁()) * (S2 #)) . (F₁(),f,G,B1)),(( the ResultSort of (F₁()) * S2) . (F₁(),f,G,B1)):]
( the Arity of (F₁()) * (S2 #)) . (F₁(),f,G,B1) is set
( the ResultSort of (F₁()) * S2) . (F₁(),f,G,B1) is set
[:(( the Arity of (F₁()) * (S2 #)) . (F₁(),f,G,B1)),(( the ResultSort of (F₁()) * S2) . (F₁(),f,G,B1)):] is Relation-like set
bool [:(( the Arity of (F₁()) * (S2 #)) . (F₁(),f,G,B1)),(( the ResultSort of (F₁()) * S2) . (F₁(),f,G,B1)):] is non empty set
o is Element of F₁()
x is Element of F₁()
a is Element of F₁()
(F₁(),o,x,a) is Element of the carrier' of (F₁())
<*o,x,a*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*o,x,a*>] is V21() set
{2,<*o,x,a*>} is non empty set
{{2,<*o,x,a*>},{2}} is non empty set
F₃(x,a) is set
F₃(o,x) is set
<*F₃(x,a),F₃(o,x)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
product <*F₃(x,a),F₃(o,x)*> is set
F₃(o,a) is set
[:(product <*F₃(x,a),F₃(o,x)*>),F₃(o,a):] is Relation-like set
bool [:(product <*F₃(x,a),F₃(o,x)*>),F₃(o,a):] is non empty set
b is Element of F₂()
c is Element of F₂()
<*c,b*> is Relation-like NAT -defined F₂() -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of F₂()
(Den ((F₁(),f,G,B1),A2)) . <*c,b*> is set
F₄(f,G,B1,c,b) is set
g is Relation-like product <*F₃(x,a),F₃(o,x)*> -defined F₃(o,a) -valued Function-like V36( product <*F₃(x,a),F₃(o,x)*>,F₃(o,a)) Element of bool [:(product <*F₃(x,a),F₃(o,x)*>),F₃(o,a):]
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier' of C1 is non empty set
C2 is strict MSAlgebra over ( the carrier of C1)
the Sorts of C2 is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
the carrier of ( the carrier of C1) is non empty set
F is strict MSAlgebra over ( the carrier of C1)
the Sorts of F is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
S1 is set
the carrier' of ( the carrier of C1) is non empty set
S2 is Element of the carrier' of ( the carrier of C1)
S2 `1 is set
A1 is Element of the carrier of C1
( the carrier of C1,A1) is Element of the carrier' of ( the carrier of C1)
<*A1*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*A1*>] is V21() set
{1,<*A1*>} is non empty set
{{1,<*A1*>},{1}} is non empty set
id A1 is Morphism of A1,A1
Hom (A1,A1) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = A1 & cod b<sub>1</sub> = A1 ) } is set
the_result_sort_of ( the carrier of C1,A1) is Element of the carrier of ( the carrier of C1)
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) . ( the carrier of C1,A1) is Element of the carrier of ( the carrier of C1)
( the carrier of C1,A1,A1) is Element of the carrier of ( the carrier of C1)
<*A1,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A1,A1*>] is V21() set
{0,<*A1,A1*>} is functional non empty set
{{0,<*A1,A1*>},{0}} is non empty set
the Sorts of C2 . ( the carrier of C1,A1,A1) is set
Result (( the carrier of C1,A1),C2) is Element of proj2 the Sorts of C2
proj2 the Sorts of C2 is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of C2) . ( the carrier of C1,A1) is set
Args (( the carrier of C1,A1),C2) is Element of proj2 ( the Sorts of C2 #)
the Sorts of C2 # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of C2 #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of C2 #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of C2 #)) . ( the carrier of C1,A1) is set
Den (( the carrier of C1,A1),C2) is Relation-like Args (( the carrier of C1,A1),C2) -defined Result (( the carrier of C1,A1),C2) -valued Function-like V36( Args (( the carrier of C1,A1),C2), Result (( the carrier of C1,A1),C2)) Element of bool [:(Args (( the carrier of C1,A1),C2)),(Result (( the carrier of C1,A1),C2)):]
[:(Args (( the carrier of C1,A1),C2)),(Result (( the carrier of C1,A1),C2)):] is Relation-like set
bool [:(Args (( the carrier of C1,A1),C2)),(Result (( the carrier of C1,A1),C2)):] is non empty set
the Charact of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of C2 #), the ResultSort of ( the carrier of C1) * the Sorts of C2
the Charact of C2 . ( the carrier of C1,A1) is Relation-like Function-like set
dom (Den (( the carrier of C1,A1),C2)) is Element of bool (Args (( the carrier of C1,A1),C2))
bool (Args (( the carrier of C1,A1),C2)) is non empty set
A2 is set
(Den (( the carrier of C1,A1),C2)) . A2 is set
Den (( the carrier of C1,A1),F) is Relation-like Args (( the carrier of C1,A1),F) -defined Result (( the carrier of C1,A1),F) -valued Function-like V36( Args (( the carrier of C1,A1),F), Result (( the carrier of C1,A1),F)) Element of bool [:(Args (( the carrier of C1,A1),F)),(Result (( the carrier of C1,A1),F)):]
Args (( the carrier of C1,A1),F) is Element of proj2 ( the Sorts of F #)
the Sorts of F # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
proj2 ( the Sorts of F #) is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of F #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of F #)) . ( the carrier of C1,A1) is set
Result (( the carrier of C1,A1),F) is Element of proj2 the Sorts of F
proj2 the Sorts of F is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of F) . ( the carrier of C1,A1) is set
[:(Args (( the carrier of C1,A1),F)),(Result (( the carrier of C1,A1),F)):] is Relation-like set
bool [:(Args (( the carrier of C1,A1),F)),(Result (( the carrier of C1,A1),F)):] is non empty set
the Charact of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of F #), the ResultSort of ( the carrier of C1) * the Sorts of F
the Charact of F . ( the carrier of C1,A1) is Relation-like Function-like set
(Den (( the carrier of C1,A1),F)) . A2 is set
the Sorts of F . ( the carrier of C1,A1,A1) is set
dom (Den (( the carrier of C1,A1),F)) is Element of bool (Args (( the carrier of C1,A1),F))
bool (Args (( the carrier of C1,A1),F)) is non empty set
the Charact of C2 . S1 is Relation-like Function-like set
the Charact of F . S1 is Relation-like Function-like set
S2 is Element of the carrier' of ( the carrier of C1)
S2 `1 is set
A1 is Element of the carrier of C1
A2 is Element of the carrier of C1
f is Element of the carrier of C1
( the carrier of C1,A1,A2,f) is Element of the carrier' of ( the carrier of C1)
<*A1,A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*A1,A2,f*>] is V21() set
{2,<*A1,A2,f*>} is non empty set
{{2,<*A1,A2,f*>},{2}} is non empty set
bool the carrier' of C1 is non empty set
Hom (A2,f) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = A2 & cod b₁ = f ) } is set
Hom (A1,A2) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = A1 & cod b₁ = A2 ) } is set
<*(Hom (A2,f)),(Hom (A1,A2))*> is Relation-like NAT -defined bool the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of bool the carrier' of C1
product <*(Hom (A2,f)),(Hom (A1,A2))*> is set
G is non empty set
the Element of G is Element of G
H is set
o is set
<*H,o*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
a is Element of the carrier' of C1
cod a is Element of the carrier of C1
x is Element of the carrier' of C1
dom x is Element of the carrier of C1
cod x is Element of the carrier of C1
x (*) a is Element of the carrier' of C1
cod (x (*) a) is Element of the carrier of C1
dom a is Element of the carrier of C1
dom (x (*) a) is Element of the carrier of C1
Hom (A1,f) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = A1 & cod b₁ = f ) } is set
G is set
B1 is set
H is set
<*B1,H*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
o is Element of the carrier' of C1
dom o is Element of the carrier of C1
cod o is Element of the carrier of C1
x is Element of the carrier' of C1
dom x is Element of the carrier of C1
cod x is Element of the carrier of C1
Den (( the carrier of C1,A1,A2,f),C2) is Relation-like Args (( the carrier of C1,A1,A2,f),C2) -defined Result (( the carrier of C1,A1,A2,f),C2) -valued Function-like V36( Args (( the carrier of C1,A1,A2,f),C2), Result (( the carrier of C1,A1,A2,f),C2)) Element of bool [:(Args (( the carrier of C1,A1,A2,f),C2)),(Result (( the carrier of C1,A1,A2,f),C2)):]
Args (( the carrier of C1,A1,A2,f),C2) is Element of proj2 ( the Sorts of C2 #)
the Sorts of C2 # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of C2 #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of C2 #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of C2 #)) . ( the carrier of C1,A1,A2,f) is set
Result (( the carrier of C1,A1,A2,f),C2) is Element of proj2 the Sorts of C2
proj2 the Sorts of C2 is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of C2) . ( the carrier of C1,A1,A2,f) is set
[:(Args (( the carrier of C1,A1,A2,f),C2)),(Result (( the carrier of C1,A1,A2,f),C2)):] is Relation-like set
bool [:(Args (( the carrier of C1,A1,A2,f),C2)),(Result (( the carrier of C1,A1,A2,f),C2)):] is non empty set
the Charact of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of C2 #), the ResultSort of ( the carrier of C1) * the Sorts of C2
the Charact of C2 . ( the carrier of C1,A1,A2,f) is Relation-like Function-like set
(Den (( the carrier of C1,A1,A2,f),C2)) . G is set
o (*) x is Element of the carrier' of C1
Den (( the carrier of C1,A1,A2,f),F) is Relation-like Args (( the carrier of C1,A1,A2,f),F) -defined Result (( the carrier of C1,A1,A2,f),F) -valued Function-like V36( Args (( the carrier of C1,A1,A2,f),F), Result (( the carrier of C1,A1,A2,f),F)) Element of bool [:(Args (( the carrier of C1,A1,A2,f),F)),(Result (( the carrier of C1,A1,A2,f),F)):]
Args (( the carrier of C1,A1,A2,f),F) is Element of proj2 ( the Sorts of F #)
the Sorts of F # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
proj2 ( the Sorts of F #) is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of F #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of F #)) . ( the carrier of C1,A1,A2,f) is set
Result (( the carrier of C1,A1,A2,f),F) is Element of proj2 the Sorts of F
proj2 the Sorts of F is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of F) . ( the carrier of C1,A1,A2,f) is set
[:(Args (( the carrier of C1,A1,A2,f),F)),(Result (( the carrier of C1,A1,A2,f),F)):] is Relation-like set
bool [:(Args (( the carrier of C1,A1,A2,f),F)),(Result (( the carrier of C1,A1,A2,f),F)):] is non empty set
the Charact of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of F #), the ResultSort of ( the carrier of C1) * the Sorts of F
the Charact of F . ( the carrier of C1,A1,A2,f) is Relation-like Function-like set
(Den (( the carrier of C1,A1,A2,f),F)) . G is set
dom (Den (( the carrier of C1,A1,A2,f),F)) is Element of bool (Args (( the carrier of C1,A1,A2,f),F))
bool (Args (( the carrier of C1,A1,A2,f),F)) is non empty set
dom (Den (( the carrier of C1,A1,A2,f),C2)) is Element of bool (Args (( the carrier of C1,A1,A2,f),C2))
bool (Args (( the carrier of C1,A1,A2,f),C2)) is non empty set
the Charact of C2 . S1 is Relation-like Function-like set
the Charact of F . S1 is Relation-like Function-like set
S2 is Element of the carrier' of ( the carrier of C1)
S2 `1 is set
the Charact of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of C2 #), the ResultSort of ( the carrier of C1) * the Sorts of C2
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Sorts of C2 # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the Arity of ( the carrier of C1) * ( the Sorts of C2 #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
the Charact of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of F #), the ResultSort of ( the carrier of C1) * the Sorts of F
the Sorts of F # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the Arity of ( the carrier of C1) * ( the Sorts of F #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
the ResultSort of ( the carrier of C1) * the Sorts of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
the Charact of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of C2 #), the ResultSort of ( the carrier of C1) * the Sorts of C2
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Sorts of C2 # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the Arity of ( the carrier of C1) * ( the Sorts of C2 #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
the Charact of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of F #), the ResultSort of ( the carrier of C1) * the Sorts of F
the Sorts of F # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the Arity of ( the carrier of C1) * ( the Sorts of F #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
the ResultSort of ( the carrier of C1) * the Sorts of F is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
S1 is set
S2 is Element of the carrier of C1
A1 is Element of the carrier of C1
( the carrier of C1,S2,A1) is Element of the carrier of ( the carrier of C1)
<*S2,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,A1*>] is V21() set
{0,<*S2,A1*>} is functional non empty set
{{0,<*S2,A1*>},{0}} is non empty set
the Sorts of C2 . S1 is set
Hom (S2,A1) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = S2 & cod b<sub>1</sub> = A1 ) } is set
the Sorts of F . S1 is set
bool the carrier' of C1 is non empty set
C2 is Element of the carrier of C1
id C2 is Morphism of C2,C2
Hom (C2,C2) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = C2 & cod b<sub>1</sub> = C2 ) } is set
S2 is Element of the carrier' of C1
C2 is Element of the carrier of C1
F is Element of the carrier of C1
Hom (C2,F) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = C2 & cod b<sub>1</sub> = F ) } is set
A1 is Element of the carrier' of C1
S1 is Element of the carrier of C1
Hom (F,S1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = F & cod b<sub>1</sub> = S1 ) } is set
cod S2 is Element of the carrier of C1
dom A1 is Element of the carrier of C1
cod A1 is Element of the carrier of C1
A1 (*) S2 is Element of the carrier' of C1
cod (A1 (*) S2) is Element of the carrier of C1
dom S2 is Element of the carrier of C1
dom (A1 (*) S2) is Element of the carrier of C1
Hom (C2,S1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = C2 & cod b<sub>1</sub> = S1 ) } is set
C2 is Element of the carrier of C1
F is Element of the carrier of C1
Hom (C2,F) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = C2 & cod b<sub>1</sub> = F ) } is set
C2 is strict MSAlgebra over ( the carrier of C1)
the Sorts of C2 is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
the carrier of ( the carrier of C1) is non empty set
A1 is Element of the carrier' of C1
dom A1 is Element of the carrier of C1
F is Element of the carrier of C1
cod A1 is Element of the carrier of C1
S1 is Element of the carrier of C1
A2 is Element of the carrier' of C1
dom A2 is Element of the carrier of C1
cod A2 is Element of the carrier of C1
S2 is Element of the carrier of C1
Hom (F,S1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = F & cod b<sub>1</sub> = S1 ) } is set
Hom (S1,S2) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = S1 & cod b<sub>1</sub> = S2 ) } is set
( the carrier of C1,F,S1,S2) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*F,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*F,S1,S2*>] is V21() set
{2,<*F,S1,S2*>} is non empty set
{{2,<*F,S1,S2*>},{2}} is non empty set
Den (( the carrier of C1,F,S1,S2),C2) is Relation-like Args (( the carrier of C1,F,S1,S2),C2) -defined Result (( the carrier of C1,F,S1,S2),C2) -valued Function-like V36( Args (( the carrier of C1,F,S1,S2),C2), Result (( the carrier of C1,F,S1,S2),C2)) Element of bool [:(Args (( the carrier of C1,F,S1,S2),C2)),(Result (( the carrier of C1,F,S1,S2),C2)):]
Args (( the carrier of C1,F,S1,S2),C2) is Element of proj2 ( the Sorts of C2 #)
the Sorts of C2 # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of C2 #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of C2 #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of C2 #)) . ( the carrier of C1,F,S1,S2) is set
Result (( the carrier of C1,F,S1,S2),C2) is Element of proj2 the Sorts of C2
proj2 the Sorts of C2 is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of C2) . ( the carrier of C1,F,S1,S2) is set
[:(Args (( the carrier of C1,F,S1,S2),C2)),(Result (( the carrier of C1,F,S1,S2),C2)):] is Relation-like set
bool [:(Args (( the carrier of C1,F,S1,S2),C2)),(Result (( the carrier of C1,F,S1,S2),C2)):] is non empty set
the Charact of C2 is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of C2 #), the ResultSort of ( the carrier of C1) * the Sorts of C2
the Charact of C2 . ( the carrier of C1,F,S1,S2) is Relation-like Function-like set
<*A2,A1*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
(Den (( the carrier of C1,F,S1,S2),C2)) . <*A2,A1*> is set
A2 (*) A1 is Element of the carrier' of C1
F is Element of the carrier of C1
S1 is Element of the carrier of C1
( the carrier of C1,F,S1) is Element of the carrier of ( the carrier of C1)
<*F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*F,S1*>] is V21() set
{0,<*F,S1*>} is functional non empty set
{{0,<*F,S1*>},{0}} is non empty set
the Sorts of C2 . ( the carrier of C1,F,S1) is set
Hom (F,S1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = F & cod b<sub>1</sub> = S1 ) } is set
S2 is Element of the carrier of C1
( the carrier of C1,S2) is Element of the carrier' of ( the carrier of C1)
<*S2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*S2*>] is V21() set
{1,<*S2*>} is non empty set
{{1,<*S2*>},{1}} is non empty set
Den (( the carrier of C1,S2),C2) is Relation-like Args (( the carrier of C1,S2),C2) -defined Result (( the carrier of C1,S2),C2) -valued Function-like V36( Args (( the carrier of C1,S2),C2), Result (( the carrier of C1,S2),C2)) Element of bool [:(Args (( the carrier of C1,S2),C2)),(Result (( the carrier of C1,S2),C2)):]
Args (( the carrier of C1,S2),C2) is Element of proj2 ( the Sorts of C2 #)
( the Arity of ( the carrier of C1) * ( the Sorts of C2 #)) . ( the carrier of C1,S2) is set
Result (( the carrier of C1,S2),C2) is Element of proj2 the Sorts of C2
( the ResultSort of ( the carrier of C1) * the Sorts of C2) . ( the carrier of C1,S2) is set
[:(Args (( the carrier of C1,S2),C2)),(Result (( the carrier of C1,S2),C2)):] is Relation-like set
bool [:(Args (( the carrier of C1,S2),C2)),(Result (( the carrier of C1,S2),C2)):] is non empty set
the Charact of C2 . ( the carrier of C1,S2) is Relation-like Function-like set
(Den (( the carrier of C1,S2),C2)) . {} is set
id S2 is Morphism of S2,S2
G is Element of the carrier' of C1
dom G is Element of the carrier of C1
A1 is Element of the carrier of C1
cod G is Element of the carrier of C1
A2 is Element of the carrier of C1
B1 is Element of the carrier' of C1
dom B1 is Element of the carrier of C1
cod B1 is Element of the carrier of C1
f is Element of the carrier of C1
( the carrier of C1,A1,A2,f) is Element of the carrier' of ( the carrier of C1)
<*A1,A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*A1,A2,f*>] is V21() set
{2,<*A1,A2,f*>} is non empty set
{{2,<*A1,A2,f*>},{2}} is non empty set
Den (( the carrier of C1,A1,A2,f),C2) is Relation-like Args (( the carrier of C1,A1,A2,f),C2) -defined Result (( the carrier of C1,A1,A2,f),C2) -valued Function-like V36( Args (( the carrier of C1,A1,A2,f),C2), Result (( the carrier of C1,A1,A2,f),C2)) Element of bool [:(Args (( the carrier of C1,A1,A2,f),C2)),(Result (( the carrier of C1,A1,A2,f),C2)):]
Args (( the carrier of C1,A1,A2,f),C2) is Element of proj2 ( the Sorts of C2 #)
( the Arity of ( the carrier of C1) * ( the Sorts of C2 #)) . ( the carrier of C1,A1,A2,f) is set
Result (( the carrier of C1,A1,A2,f),C2) is Element of proj2 the Sorts of C2
( the ResultSort of ( the carrier of C1) * the Sorts of C2) . ( the carrier of C1,A1,A2,f) is set
[:(Args (( the carrier of C1,A1,A2,f),C2)),(Result (( the carrier of C1,A1,A2,f),C2)):] is Relation-like set
bool [:(Args (( the carrier of C1,A1,A2,f),C2)),(Result (( the carrier of C1,A1,A2,f),C2)):] is non empty set
the Charact of C2 . ( the carrier of C1,A1,A2,f) is Relation-like Function-like set
<*B1,G*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
(Den (( the carrier of C1,A1,A2,f),C2)) . <*B1,G*> is set
B1 (*) G is Element of the carrier' of C1
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict MSAlgebra over ( the carrier of C1)
C2 is Element of the carrier of C1
( the carrier of C1,C2) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*C2*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*C2*>] is V21() set
{1,<*C2*>} is non empty set
{{1,<*C2*>},{1}} is non empty set
Result (( the carrier of C1,C2),(C1)) is Element of proj2 the Sorts of (C1)
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
the carrier of ( the carrier of C1) is non empty set
proj2 the Sorts of (C1) is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2) is set
Hom (C2,C2) is Element of bool the carrier' of C1
the carrier' of C1 is non empty set
bool the carrier' of C1 is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = C2 & cod b<sub>1</sub> = C2 ) } is set
the_result_sort_of ( the carrier of C1,C2) is Element of the carrier of ( the carrier of C1)
the ResultSort of ( the carrier of C1) . ( the carrier of C1,C2) is Element of the carrier of ( the carrier of C1)
the Sorts of (C1) . (the_result_sort_of ( the carrier of C1,C2)) is set
( the carrier of C1,C2,C2) is Element of the carrier of ( the carrier of C1)
<*C2,C2*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*C2,C2*>] is V21() set
{0,<*C2,C2*>} is functional non empty set
{{0,<*C2,C2*>},{0}} is non empty set
the Sorts of (C1) . ( the carrier of C1,C2,C2) is set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict MSAlgebra over ( the carrier of C1)
the carrier' of C1 is non empty set
bool the carrier' of C1 is non empty set
C2 is Element of the carrier of C1
F is Element of the carrier of C1
S1 is Element of the carrier of C1
( the carrier of C1,C2,F,S1) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*C2,F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,S1*>] is V21() set
{2,<*C2,F,S1*>} is non empty set
{{2,<*C2,F,S1*>},{2}} is non empty set
Args (( the carrier of C1,C2,F,S1),(C1)) is Element of proj2 ( the Sorts of (C1) #)
the carrier of ( the carrier of C1) is non empty set
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,F,S1) is set
Hom (F,S1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = F & cod b<sub>1</sub> = S1 ) } is set
Hom (C2,F) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = C2 & cod b<sub>1</sub> = F ) } is set
<*(Hom (F,S1)),(Hom (C2,F))*> is Relation-like NAT -defined bool the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of bool the carrier' of C1
product <*(Hom (F,S1)),(Hom (C2,F))*> is set
Result (( the carrier of C1,C2,F,S1),(C1)) is Element of proj2 the Sorts of (C1)
proj2 the Sorts of (C1) is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2,F,S1) is set
Hom (C2,S1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = C2 & cod b<sub>1</sub> = S1 ) } is set
S2 is Element of the carrier of C1
A1 is Element of the carrier of C1
( the carrier of C1,S2,A1) is Element of the carrier of ( the carrier of C1)
<*S2,A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*S2,A1*>] is V21() set
{0,<*S2,A1*>} is functional non empty set
{{0,<*S2,A1*>},{0}} is non empty set
the Sorts of (C1) . ( the carrier of C1,S2,A1) is set
Hom (S2,A1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = S2 & cod b<sub>1</sub> = A1 ) } is set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict MSAlgebra over ( the carrier of C1)
C2 is set
F is set
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
the carrier of ( the carrier of C1) is non empty set
the Sorts of (C1) . C2 is set
the Sorts of (C1) . F is set
S1 is set
dom the Sorts of (C1) is non empty Element of bool the carrier of ( the carrier of C1)
bool the carrier of ( the carrier of C1) is non empty set
S2 is Element of the carrier of ( the carrier of C1)
A2 is Element of the carrier of C1
f is Element of the carrier of C1
( the carrier of C1,A2,f) is Element of the carrier of ( the carrier of C1)
<*A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A2,f*>] is V21() set
{0,<*A2,f*>} is functional non empty set
{{0,<*A2,f*>},{0}} is non empty set
Hom (A2,f) is Element of bool the carrier' of C1
the carrier' of C1 is non empty set
bool the carrier' of C1 is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = A2 & cod b<sub>1</sub> = f ) } is set
A1 is Element of the carrier of ( the carrier of C1)
G is Element of the carrier of C1
B1 is Element of the carrier of C1
( the carrier of C1,G,B1) is Element of the carrier of ( the carrier of C1)
<*G,B1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*G,B1*>] is V21() set
{0,<*G,B1*>} is functional non empty set
{{0,<*G,B1*>},{0}} is non empty set
Hom (G,B1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = G & cod b<sub>1</sub> = B1 ) } is set
H is Element of the carrier' of C1
dom H is Element of the carrier of C1
cod H is Element of the carrier of C1
the carrier' of ( the carrier of C1) is non empty set
C2 is Element of the carrier' of ( the carrier of C1)
Args (C2,(C1)) is Element of proj2 ( the Sorts of (C1) #)
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . C2 is set
Result (C2,(C1)) is Element of proj2 the Sorts of (C1)
proj2 the Sorts of (C1) is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . C2 is set
C2 `1 is set
F is Element of the carrier of C1
( the carrier of C1,F) is Element of the carrier' of ( the carrier of C1)
<*F*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*F*>] is V21() set
{1,<*F*>} is non empty set
{{1,<*F*>},{1}} is non empty set
Hom (F,F) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = F ) } is set
C2 `1 is set
F is Element of the carrier of C1
S1 is Element of the carrier of C1
S2 is Element of the carrier of C1
( the carrier of C1,F,S1,S2) is Element of the carrier' of ( the carrier of C1)
<*F,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*F,S1,S2*>] is V21() set
{2,<*F,S1,S2*>} is non empty set
{{2,<*F,S1,S2*>},{2}} is non empty set
the Element of Args (C2,(C1)) is Element of Args (C2,(C1))
Hom (S1,S2) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = S1 & cod b<sub>1</sub> = S2 ) } is set
Hom (F,S1) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = F & cod b<sub>1</sub> = S1 ) } is set
<*(Hom (S1,S2)),(Hom (F,S1))*> is Relation-like NAT -defined bool the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of bool the carrier' of C1
product <*(Hom (S1,S2)),(Hom (F,S1))*> is set
Hom (F,S2) is Element of bool the carrier' of C1
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = F & cod b<sub>1</sub> = S2 ) } is set
A2 is set
f is set
<*A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
C2 `1 is set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier of ( the carrier of C1) is non empty set
(C1) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C1)
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total V131() set
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
(C2) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C2)
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
( the carrier of ( the carrier of C1), the Sorts of (C1),F) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() set
(C1,C2,F) is Relation-like the carrier of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):]
the carrier of ( the carrier of C2) is non empty set
[: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
(C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
the carrier' of ( the carrier of C1) is non empty set
the carrier' of ( the carrier of C2) is non empty set
[: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is non empty set
(C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)) is strict MSAlgebra over ( the carrier of C1)
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
o is set
( the carrier of ( the carrier of C1), the Sorts of (C1),F) . o is Relation-like Function-like set
the Sorts of (C1) . o is set
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . o is set
[:( the Sorts of (C1) . o),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . o):] is Relation-like set
bool [:( the Sorts of (C1) . o),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . o):] is non empty set
x is Element of the carrier of ( the carrier of C1)
a is Element of the carrier of C1
b is Element of the carrier of C1
( the carrier of C1,a,b) is Element of the carrier of ( the carrier of C1)
<*a,b*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*a,b*>] is V21() set
{0,<*a,b*>} is functional non empty set
{{0,<*a,b*>},{0}} is non empty set
the Sorts of (C2) is Relation-like the carrier of ( the carrier of C2) -defined Function-like non empty total V131() set
(C1,C2,F) * the Sorts of (C2) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
(C1,C2,F) . x is Element of the carrier of ( the carrier of C2)
the Sorts of (C2) . ((C1,C2,F) . x) is set
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . x is set
F . a is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . a is Element of the carrier of C2
F . b is Element of the carrier of C2
(Obj F) . b is Element of the carrier of C2
( the carrier of C2,(F . a),(F . b)) is Element of the carrier of ( the carrier of C2)
<*(F . a),(F . b)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*(F . a),(F . b)*>] is V21() set
{0,<*(F . a),(F . b)*>} is functional non empty set
{{0,<*(F . a),(F . b)*>},{0}} is non empty set
Hom ((F . a),(F . b)) is Element of bool the carrier' of C2
bool the carrier' of C2 is non empty set
{ b₁ where b₁ is Element of the carrier' of C2 : ( dom b₁ = F . a & cod b₁ = F . b ) } is set
the Sorts of (C1) . x is set
Hom (a,b) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = a & cod b₁ = b ) } is set
( the carrier of ( the carrier of C1), the Sorts of (C1),F) . x is Relation-like Function-like set
F | ( the Sorts of (C1) . x) is Relation-like the carrier' of C1 -defined the Sorts of (C1) . x -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
[: the carrier' of C1, the carrier' of C2:] is Relation-like non empty set
bool [: the carrier' of C1, the carrier' of C2:] is non empty set
hom (F,a,b) is Relation-like Hom (a,b) -defined Hom ((F . a),(F . b)) -valued Function-like V36( Hom (a,b), Hom ((F . a),(F . b))) Element of bool [:(Hom (a,b)),(Hom ((F . a),(F . b))):]
[:(Hom (a,b)),(Hom ((F . a),(F . b))):] is Relation-like set
bool [:(Hom (a,b)),(Hom ((F . a),(F . b))):] is non empty set
F | (Hom (a,b)) is Relation-like the carrier' of C1 -defined Hom (a,b) -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C1)
the carrier' of C1 is non empty set
C2 is Element of the carrier of C1
F is Element of the carrier of C1
S1 is Element of the carrier of C1
( the carrier of C1,C2,F,S1) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*C2,F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,S1*>] is V21() set
{2,<*C2,F,S1*>} is non empty set
{{2,<*C2,F,S1*>},{2}} is non empty set
Args (( the carrier of C1,C2,F,S1),(C1)) is Element of proj2 ( the Sorts of (C1) #)
the carrier of ( the carrier of C1) is non empty set
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total V131() set
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,F,S1) is set
S2 is set
A2 is Element of the carrier of C1
f is Element of the carrier of C1
( the carrier of C1,A2,f) is Element of the carrier of ( the carrier of C1)
<*A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*A2,f*>] is V21() set
{0,<*A2,f*>} is functional non empty set
{{0,<*A2,f*>},{0}} is non empty set
the Sorts of (C1) . ( the carrier of C1,A2,f) is set
Hom (A2,f) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = A2 & cod b₁ = f ) } is set
bool the carrier' of C1 is non empty set
Hom (F,S1) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = S1 ) } is set
Hom (C2,F) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = C2 & cod b₁ = F ) } is set
<*(Hom (F,S1)),(Hom (C2,F))*> is Relation-like NAT -defined bool the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of bool the carrier' of C1
product <*(Hom (F,S1)),(Hom (C2,F))*> is set
A2 is set
f is set
<*A2,f*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
G is Element of the carrier' of C1
B1 is Element of the carrier' of C1
H is Element of the carrier' of C1
o is Element of the carrier' of C1
<*H,o*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
dom o is Element of the carrier of C1
cod o is Element of the carrier of C1
dom H is Element of the carrier of C1
cod H is Element of the carrier of C1
A2 is Element of the carrier' of C1
f is Element of the carrier' of C1
<*A2,f*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
dom f is Element of the carrier of C1
cod f is Element of the carrier of C1
dom A2 is Element of the carrier of C1
cod A2 is Element of the carrier of C1
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C1)
the carrier of ( the carrier of C1) is non empty set
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total V131() set
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
(C2) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C2)
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
(C1,C2,F) is Relation-like the carrier of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):]
the carrier of ( the carrier of C2) is non empty set
[: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
(C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
the carrier' of ( the carrier of C1) is non empty set
the carrier' of ( the carrier of C2) is non empty set
[: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is non empty set
(C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)) is strict MSAlgebra over ( the carrier of C1)
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
( the carrier of ( the carrier of C1), the Sorts of (C1),F) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() set
H is Element of the carrier of C1
o is Element of the carrier of C1
Hom (H,o) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = H & cod b₁ = o ) } is set
x is Element of the carrier of C1
Hom (o,x) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = o & cod b₁ = x ) } is set
( the carrier of C1,H,o,x) is Element of the carrier' of ( the carrier of C1)
<*H,o,x*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*H,o,x*>] is V21() set
{2,<*H,o,x*>} is non empty set
{{2,<*H,o,x*>},{2}} is non empty set
Args (( the carrier of C1,H,o,x),(C1)) is Element of proj2 ( the Sorts of (C1) #)
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,H,o,x) is set
b is Element of the carrier' of C1
c is Element of the carrier' of C1
<*c,b*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
F . c is Element of the carrier' of C2
F . b is Element of the carrier' of C2
<*(F . c),(F . b)*> is Relation-like NAT -defined the carrier' of C2 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C2
g is Element of Args (( the carrier of C1,H,o,x),(C1))
F . o is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . o is Element of the carrier of C2
F . x is Element of the carrier of C2
(Obj F) . x is Element of the carrier of C2
Hom ((F . o),(F . x)) is Element of bool the carrier' of C2
bool the carrier' of C2 is non empty set
{ b₁ where b₁ is Element of the carrier' of C2 : ( dom b₁ = F . o & cod b₁ = F . x ) } is set
dom (F . c) is Element of the carrier of C2
cod (F . c) is Element of the carrier of C2
F . H is Element of the carrier of C2
(Obj F) . H is Element of the carrier of C2
Hom ((F . H),(F . o)) is Element of bool the carrier' of C2
{ b₁ where b₁ is Element of the carrier' of C2 : ( dom b₁ = F . H & cod b₁ = F . o ) } is set
dom (F . b) is Element of the carrier of C2
cod (F . b) is Element of the carrier of C2
( the carrier of C2,(F . H),(F . o),(F . x)) is Element of the carrier' of ( the carrier of C2)
<*(F . H),(F . o),(F . x)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*(F . H),(F . o),(F . x)*>] is V21() set
{2,<*(F . H),(F . o),(F . x)*>} is non empty set
{{2,<*(F . H),(F . o),(F . x)*>},{2}} is non empty set
Args (( the carrier of C2,(F . H),(F . o),(F . x)),(C2)) is Element of proj2 ( the Sorts of (C2) #)
the Sorts of (C2) is Relation-like the carrier of ( the carrier of C2) -defined Function-like non empty total V131() set
the Sorts of (C2) # is Relation-like the carrier of ( the carrier of C2) * -defined Function-like non empty total set
the carrier of ( the carrier of C2) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C2)
proj2 ( the Sorts of (C2) #) is non empty set
the Arity of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C2) -defined the carrier of ( the carrier of C2) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):]
[: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is non empty set
the Arity of ( the carrier of C2) * ( the Sorts of (C2) #) is Relation-like the carrier' of ( the carrier of C2) -defined Function-like non empty total set
( the Arity of ( the carrier of C2) * ( the Sorts of (C2) #)) . ( the carrier of C2,(F . H),(F . o),(F . x)) is set
dom c is Element of the carrier of C1
cod c is Element of the carrier of C1
dom b is Element of the carrier of C1
cod b is Element of the carrier of C1
h is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Sorts of (C1), the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))
h # g is Element of Args (( the carrier of C1,H,o,x),((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))
Args (( the carrier of C1,H,o,x),((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))) is Element of proj2 ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #)
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
proj2 ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #) is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #)) . ( the carrier of C1,H,o,x) is set
( the carrier of C1,o,x) is Element of the carrier of ( the carrier of C1)
<*o,x*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*o,x*>] is V21() set
{0,<*o,x*>} is functional non empty set
{{0,<*o,x*>},{0}} is non empty set
the Sorts of (C1) . ( the carrier of C1,o,x) is set
h . ( the carrier of C1,o,x) is Relation-like the Sorts of (C1) . ( the carrier of C1,o,x) -defined the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,o,x) -valued Function-like V36( the Sorts of (C1) . ( the carrier of C1,o,x), the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,o,x)) Element of bool [:( the Sorts of (C1) . ( the carrier of C1,o,x)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,o,x)):]
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,o,x) is set
[:( the Sorts of (C1) . ( the carrier of C1,o,x)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,o,x)):] is Relation-like set
bool [:( the Sorts of (C1) . ( the carrier of C1,o,x)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,o,x)):] is non empty set
F | (Hom (o,x)) is Relation-like the carrier' of C1 -defined Hom (o,x) -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
[: the carrier' of C1, the carrier' of C2:] is Relation-like non empty set
bool [: the carrier' of C1, the carrier' of C2:] is non empty set
(h . ( the carrier of C1,o,x)) . c is set
dom <*c,b*> is non empty Element of bool NAT
( the carrier of C1,H,o) is Element of the carrier of ( the carrier of C1)
<*H,o*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*H,o*>] is V21() set
{0,<*H,o*>} is functional non empty set
{{0,<*H,o*>},{0}} is non empty set
the Sorts of (C1) . ( the carrier of C1,H,o) is set
h . ( the carrier of C1,H,o) is Relation-like the Sorts of (C1) . ( the carrier of C1,H,o) -defined the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,H,o) -valued Function-like V36( the Sorts of (C1) . ( the carrier of C1,H,o), the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,H,o)) Element of bool [:( the Sorts of (C1) . ( the carrier of C1,H,o)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,H,o)):]
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,H,o) is set
[:( the Sorts of (C1) . ( the carrier of C1,H,o)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,H,o)):] is Relation-like set
bool [:( the Sorts of (C1) . ( the carrier of C1,H,o)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,H,o)):] is non empty set
F | (Hom (H,o)) is Relation-like the carrier' of C1 -defined Hom (H,o) -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
(h . ( the carrier of C1,H,o)) . b is set
(C1,C2,F) . ( the carrier of C1,H,o,x) is Element of the carrier' of ( the carrier of C2)
Args (((C1,C2,F) . ( the carrier of C1,H,o,x)),(C2)) is Element of proj2 ( the Sorts of (C2) #)
( the Arity of ( the carrier of C2) * ( the Sorts of (C2) #)) . ((C1,C2,F) . ( the carrier of C1,H,o,x)) is set
gh is Element of the carrier' of C2
f9 is Element of the carrier' of C2
<*gh,f9*> is Relation-like NAT -defined the carrier' of C2 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C2
dom f9 is Element of the carrier of C2
cod f9 is Element of the carrier of C2
dom gh is Element of the carrier of C2
cod gh is Element of the carrier of C2
<*gh,f9*> . 1 is set
the_arity_of ( the carrier of C1,H,o,x) is Relation-like NAT -defined the carrier of ( the carrier of C1) -valued Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C1) *
the Arity of ( the carrier of C1) . ( the carrier of C1,H,o,x) is Relation-like NAT -defined Function-like V24() FinSequence-like FinSubsequence-like Element of the carrier of ( the carrier of C1) *
<*( the carrier of C1,o,x),( the carrier of C1,H,o)*> is Relation-like NAT -defined the carrier of ( the carrier of C1) -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of C1)
<*c,b*> . 1 is set
(the_arity_of ( the carrier of C1,H,o,x)) /. 1 is Element of the carrier of ( the carrier of C1)
<*c,b*> . 2 is set
(the_arity_of ( the carrier of C1,H,o,x)) /. 2 is Element of the carrier of ( the carrier of C1)
<*gh,f9*> . 2 is set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
the carrier' of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C1)
C2 is Element of the carrier of C1
F is Element of the carrier of C1
Hom (C2,F) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = C2 & cod b₁ = F ) } is set
S1 is Element of the carrier of C1
Hom (F,S1) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = S1 ) } is set
( the carrier of C1,C2,F,S1) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*C2,F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,S1*>] is V21() set
{2,<*C2,F,S1*>} is non empty set
{{2,<*C2,F,S1*>},{2}} is non empty set
Den (( the carrier of C1,C2,F,S1),(C1)) is Relation-like Args (( the carrier of C1,C2,F,S1),(C1)) -defined Result (( the carrier of C1,C2,F,S1),(C1)) -valued Function-like V36( Args (( the carrier of C1,C2,F,S1),(C1)), Result (( the carrier of C1,C2,F,S1),(C1))) Element of bool [:(Args (( the carrier of C1,C2,F,S1),(C1))),(Result (( the carrier of C1,C2,F,S1),(C1))):]
Args (( the carrier of C1,C2,F,S1),(C1)) is Element of proj2 ( the Sorts of (C1) #)
the carrier of ( the carrier of C1) is non empty set
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total V131() set
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,F,S1) is set
Result (( the carrier of C1,C2,F,S1),(C1)) is Element of proj2 the Sorts of (C1)
proj2 the Sorts of (C1) is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2,F,S1) is set
[:(Args (( the carrier of C1,C2,F,S1),(C1))),(Result (( the carrier of C1,C2,F,S1),(C1))):] is Relation-like set
bool [:(Args (( the carrier of C1,C2,F,S1),(C1))),(Result (( the carrier of C1,C2,F,S1),(C1))):] is non empty set
the Charact of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of (C1) #), the ResultSort of ( the carrier of C1) * the Sorts of (C1)
the Charact of (C1) . ( the carrier of C1,C2,F,S1) is Relation-like Function-like set
S2 is Element of the carrier' of C1
A1 is Element of the carrier' of C1
<*A1,S2*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
(Den (( the carrier of C1,C2,F,S1),(C1))) . <*A1,S2*> is set
A1 (*) S2 is Element of the carrier' of C1
dom A1 is Element of the carrier of C1
cod A1 is Element of the carrier of C1
dom S2 is Element of the carrier of C1
cod S2 is Element of the carrier of C1
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
the carrier' of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C1)
C2 is Element of the carrier of C1
F is Element of the carrier of C1
Hom (C2,F) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = C2 & cod b₁ = F ) } is set
S1 is Element of the carrier of C1
Hom (F,S1) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = S1 ) } is set
S2 is Element of the carrier of C1
Hom (S1,S2) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = S1 & cod b₁ = S2 ) } is set
( the carrier of C1,C2,S1,S2) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*C2,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,S1,S2*>] is V21() set
{2,<*C2,S1,S2*>} is non empty set
{{2,<*C2,S1,S2*>},{2}} is non empty set
Den (( the carrier of C1,C2,S1,S2),(C1)) is Relation-like Args (( the carrier of C1,C2,S1,S2),(C1)) -defined Result (( the carrier of C1,C2,S1,S2),(C1)) -valued Function-like V36( Args (( the carrier of C1,C2,S1,S2),(C1)), Result (( the carrier of C1,C2,S1,S2),(C1))) Element of bool [:(Args (( the carrier of C1,C2,S1,S2),(C1))),(Result (( the carrier of C1,C2,S1,S2),(C1))):]
Args (( the carrier of C1,C2,S1,S2),(C1)) is Element of proj2 ( the Sorts of (C1) #)
the carrier of ( the carrier of C1) is non empty set
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total V131() set
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,S1,S2) is set
Result (( the carrier of C1,C2,S1,S2),(C1)) is Element of proj2 the Sorts of (C1)
proj2 the Sorts of (C1) is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2,S1,S2) is set
[:(Args (( the carrier of C1,C2,S1,S2),(C1))),(Result (( the carrier of C1,C2,S1,S2),(C1))):] is Relation-like set
bool [:(Args (( the carrier of C1,C2,S1,S2),(C1))),(Result (( the carrier of C1,C2,S1,S2),(C1))):] is non empty set
the Charact of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of (C1) #), the ResultSort of ( the carrier of C1) * the Sorts of (C1)
the Charact of (C1) . ( the carrier of C1,C2,S1,S2) is Relation-like Function-like set
( the carrier of C1,C2,F,S1) is Element of the carrier' of ( the carrier of C1)
<*C2,F,S1*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,S1*>] is V21() set
{2,<*C2,F,S1*>} is non empty set
{{2,<*C2,F,S1*>},{2}} is non empty set
Den (( the carrier of C1,C2,F,S1),(C1)) is Relation-like Args (( the carrier of C1,C2,F,S1),(C1)) -defined Result (( the carrier of C1,C2,F,S1),(C1)) -valued Function-like V36( Args (( the carrier of C1,C2,F,S1),(C1)), Result (( the carrier of C1,C2,F,S1),(C1))) Element of bool [:(Args (( the carrier of C1,C2,F,S1),(C1))),(Result (( the carrier of C1,C2,F,S1),(C1))):]
Args (( the carrier of C1,C2,F,S1),(C1)) is Element of proj2 ( the Sorts of (C1) #)
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,F,S1) is set
Result (( the carrier of C1,C2,F,S1),(C1)) is Element of proj2 the Sorts of (C1)
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2,F,S1) is set
[:(Args (( the carrier of C1,C2,F,S1),(C1))),(Result (( the carrier of C1,C2,F,S1),(C1))):] is Relation-like set
bool [:(Args (( the carrier of C1,C2,F,S1),(C1))),(Result (( the carrier of C1,C2,F,S1),(C1))):] is non empty set
the Charact of (C1) . ( the carrier of C1,C2,F,S1) is Relation-like Function-like set
( the carrier of C1,C2,F,S2) is Element of the carrier' of ( the carrier of C1)
<*C2,F,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,S2*>] is V21() set
{2,<*C2,F,S2*>} is non empty set
{{2,<*C2,F,S2*>},{2}} is non empty set
Den (( the carrier of C1,C2,F,S2),(C1)) is Relation-like Args (( the carrier of C1,C2,F,S2),(C1)) -defined Result (( the carrier of C1,C2,F,S2),(C1)) -valued Function-like V36( Args (( the carrier of C1,C2,F,S2),(C1)), Result (( the carrier of C1,C2,F,S2),(C1))) Element of bool [:(Args (( the carrier of C1,C2,F,S2),(C1))),(Result (( the carrier of C1,C2,F,S2),(C1))):]
Args (( the carrier of C1,C2,F,S2),(C1)) is Element of proj2 ( the Sorts of (C1) #)
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,F,S2) is set
Result (( the carrier of C1,C2,F,S2),(C1)) is Element of proj2 the Sorts of (C1)
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2,F,S2) is set
[:(Args (( the carrier of C1,C2,F,S2),(C1))),(Result (( the carrier of C1,C2,F,S2),(C1))):] is Relation-like set
bool [:(Args (( the carrier of C1,C2,F,S2),(C1))),(Result (( the carrier of C1,C2,F,S2),(C1))):] is non empty set
the Charact of (C1) . ( the carrier of C1,C2,F,S2) is Relation-like Function-like set
( the carrier of C1,F,S1,S2) is Element of the carrier' of ( the carrier of C1)
<*F,S1,S2*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*F,S1,S2*>] is V21() set
{2,<*F,S1,S2*>} is non empty set
{{2,<*F,S1,S2*>},{2}} is non empty set
Den (( the carrier of C1,F,S1,S2),(C1)) is Relation-like Args (( the carrier of C1,F,S1,S2),(C1)) -defined Result (( the carrier of C1,F,S1,S2),(C1)) -valued Function-like V36( Args (( the carrier of C1,F,S1,S2),(C1)), Result (( the carrier of C1,F,S1,S2),(C1))) Element of bool [:(Args (( the carrier of C1,F,S1,S2),(C1))),(Result (( the carrier of C1,F,S1,S2),(C1))):]
Args (( the carrier of C1,F,S1,S2),(C1)) is Element of proj2 ( the Sorts of (C1) #)
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,F,S1,S2) is set
Result (( the carrier of C1,F,S1,S2),(C1)) is Element of proj2 the Sorts of (C1)
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,F,S1,S2) is set
[:(Args (( the carrier of C1,F,S1,S2),(C1))),(Result (( the carrier of C1,F,S1,S2),(C1))):] is Relation-like set
bool [:(Args (( the carrier of C1,F,S1,S2),(C1))),(Result (( the carrier of C1,F,S1,S2),(C1))):] is non empty set
the Charact of (C1) . ( the carrier of C1,F,S1,S2) is Relation-like Function-like set
A1 is Element of the carrier' of C1
A2 is Element of the carrier' of C1
f is Element of the carrier' of C1
<*A2,A1*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
(Den (( the carrier of C1,C2,F,S1),(C1))) . <*A2,A1*> is set
<*f,((Den (( the carrier of C1,C2,F,S1),(C1))) . <*A2,A1*>)*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
(Den (( the carrier of C1,C2,S1,S2),(C1))) . <*f,((Den (( the carrier of C1,C2,F,S1),(C1))) . <*A2,A1*>)*> is set
<*f,A2*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
(Den (( the carrier of C1,F,S1,S2),(C1))) . <*f,A2*> is set
<*((Den (( the carrier of C1,F,S1,S2),(C1))) . <*f,A2*>),A1*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
(Den (( the carrier of C1,C2,F,S2),(C1))) . <*((Den (( the carrier of C1,F,S1,S2),(C1))) . <*f,A2*>),A1*> is set
cod A2 is Element of the carrier of C1
f (*) A2 is Element of the carrier' of C1
cod A1 is Element of the carrier of C1
dom f is Element of the carrier of C1
cod f is Element of the carrier of C1
cod (f (*) A2) is Element of the carrier of C1
dom A2 is Element of the carrier of C1
dom (f (*) A2) is Element of the carrier of C1
Hom (F,S2) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = S2 ) } is set
dom A1 is Element of the carrier of C1
A2 (*) A1 is Element of the carrier' of C1
dom (A2 (*) A1) is Element of the carrier of C1
cod (A2 (*) A1) is Element of the carrier of C1
Hom (C2,S1) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = C2 & cod b₁ = S1 ) } is set
f (*) (A2 (*) A1) is Element of the carrier' of C1
(f (*) A2) (*) A1 is Element of the carrier' of C1
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier of C1 is non empty set
the carrier' of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
(C1) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C1)
C2 is Element of the carrier of C1
F is Element of the carrier of C1
Hom (C2,F) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = C2 & cod b₁ = F ) } is set
( the carrier of C1,C2,F,F) is Element of the carrier' of ( the carrier of C1)
the carrier' of ( the carrier of C1) is non empty set
<*C2,F,F*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,F,F*>] is V21() set
{2,<*C2,F,F*>} is non empty set
{{2,<*C2,F,F*>},{2}} is non empty set
Den (( the carrier of C1,C2,F,F),(C1)) is Relation-like Args (( the carrier of C1,C2,F,F),(C1)) -defined Result (( the carrier of C1,C2,F,F),(C1)) -valued Function-like V36( Args (( the carrier of C1,C2,F,F),(C1)), Result (( the carrier of C1,C2,F,F),(C1))) Element of bool [:(Args (( the carrier of C1,C2,F,F),(C1))),(Result (( the carrier of C1,C2,F,F),(C1))):]
Args (( the carrier of C1,C2,F,F),(C1)) is Element of proj2 ( the Sorts of (C1) #)
the carrier of ( the carrier of C1) is non empty set
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total V131() set
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,F,F) is set
Result (( the carrier of C1,C2,F,F),(C1)) is Element of proj2 the Sorts of (C1)
proj2 the Sorts of (C1) is non empty set
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2,F,F) is set
[:(Args (( the carrier of C1,C2,F,F),(C1))),(Result (( the carrier of C1,C2,F,F),(C1))):] is Relation-like set
bool [:(Args (( the carrier of C1,C2,F,F),(C1))),(Result (( the carrier of C1,C2,F,F),(C1))):] is non empty set
the Charact of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of (C1) #), the ResultSort of ( the carrier of C1) * the Sorts of (C1)
the Charact of (C1) . ( the carrier of C1,C2,F,F) is Relation-like Function-like set
id F is Morphism of F,F
( the carrier of C1,C2,C2,F) is Element of the carrier' of ( the carrier of C1)
<*C2,C2,F*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*C2,C2,F*>] is V21() set
{2,<*C2,C2,F*>} is non empty set
{{2,<*C2,C2,F*>},{2}} is non empty set
Den (( the carrier of C1,C2,C2,F),(C1)) is Relation-like Args (( the carrier of C1,C2,C2,F),(C1)) -defined Result (( the carrier of C1,C2,C2,F),(C1)) -valued Function-like V36( Args (( the carrier of C1,C2,C2,F),(C1)), Result (( the carrier of C1,C2,C2,F),(C1))) Element of bool [:(Args (( the carrier of C1,C2,C2,F),(C1))),(Result (( the carrier of C1,C2,C2,F),(C1))):]
Args (( the carrier of C1,C2,C2,F),(C1)) is Element of proj2 ( the Sorts of (C1) #)
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . ( the carrier of C1,C2,C2,F) is set
Result (( the carrier of C1,C2,C2,F),(C1)) is Element of proj2 the Sorts of (C1)
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . ( the carrier of C1,C2,C2,F) is set
[:(Args (( the carrier of C1,C2,C2,F),(C1))),(Result (( the carrier of C1,C2,C2,F),(C1))):] is Relation-like set
bool [:(Args (( the carrier of C1,C2,C2,F),(C1))),(Result (( the carrier of C1,C2,C2,F),(C1))):] is non empty set
the Charact of (C1) . ( the carrier of C1,C2,C2,F) is Relation-like Function-like set
id C2 is Morphism of C2,C2
S1 is Element of the carrier' of C1
<*(id F),S1*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
(Den (( the carrier of C1,C2,F,F),(C1))) . <*(id F),S1*> is set
<*S1,(id C2)*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
(Den (( the carrier of C1,C2,C2,F),(C1))) . <*S1,(id C2)*> is set
dom S1 is Element of the carrier of C1
S1 (*) (id C2) is Element of the carrier' of C1
cod S1 is Element of the carrier of C1
(id F) (*) S1 is Element of the carrier' of C1
Hom (F,F) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = F & cod b₁ = F ) } is set
Hom (C2,C2) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = C2 & cod b₁ = C2 ) } is set
C1 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C1 is non empty set
C2 is non empty non void feasible Category-like V65() V66() V67() with_identities CatStr
the carrier' of C2 is non empty set
the carrier of C1 is non empty set
( the carrier of C1) is non empty non void feasible strict feasible () () ( the carrier of C1)
the carrier of ( the carrier of C1) is non empty set
(C1) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C1)
the Sorts of (C1) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total V131() set
the carrier of C2 is non empty set
( the carrier of C2) is non empty non void feasible strict feasible () () ( the carrier of C2)
(C2) is strict disjoint_valued feasible MSAlgebra over ( the carrier of C2)
F is Relation-like the carrier' of C1 -defined the carrier' of C2 -valued Function-like non empty total V36( the carrier' of C1, the carrier' of C2) Functor of C1,C2
(C1,C2,F) is Relation-like the carrier of ( the carrier of C1) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier of ( the carrier of C1), the carrier of ( the carrier of C2)) Element of bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):]
the carrier of ( the carrier of C2) is non empty set
[: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier of ( the carrier of C1), the carrier of ( the carrier of C2):] is non empty set
(C1,C2,F) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier' of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):]
the carrier' of ( the carrier of C1) is non empty set
the carrier' of ( the carrier of C2) is non empty set
[: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier' of ( the carrier of C2):] is non empty set
(C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)) is strict MSAlgebra over ( the carrier of C1)
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total set
( the carrier of ( the carrier of C1), the Sorts of (C1),F) is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() set
H is Relation-like the carrier of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Sorts of (C1), the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))
o is Element of the carrier' of ( the carrier of C1)
Args (o,(C1)) is Element of proj2 ( the Sorts of (C1) #)
the Sorts of (C1) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
the carrier of ( the carrier of C1) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C1)
proj2 ( the Sorts of (C1) #) is non empty set
the Arity of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):]
[: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1),( the carrier of ( the carrier of C1) *):] is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of (C1) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of (C1) #)) . o is set
the_result_sort_of o is Element of the carrier of ( the carrier of C1)
the ResultSort of ( the carrier of C1) is Relation-like the carrier' of ( the carrier of C1) -defined the carrier of ( the carrier of C1) -valued Function-like non empty total V36( the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1)) Element of bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):]
[: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C1), the carrier of ( the carrier of C1):] is non empty set
the ResultSort of ( the carrier of C1) . o is Element of the carrier of ( the carrier of C1)
H . (the_result_sort_of o) is Relation-like the Sorts of (C1) . (the_result_sort_of o) -defined the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . (the_result_sort_of o) -valued Function-like V36( the Sorts of (C1) . (the_result_sort_of o), the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . (the_result_sort_of o)) Element of bool [:( the Sorts of (C1) . (the_result_sort_of o)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . (the_result_sort_of o)):]
the Sorts of (C1) . (the_result_sort_of o) is set
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . (the_result_sort_of o) is set
[:( the Sorts of (C1) . (the_result_sort_of o)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . (the_result_sort_of o)):] is Relation-like set
bool [:( the Sorts of (C1) . (the_result_sort_of o)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . (the_result_sort_of o)):] is non empty set
Den (o,(C1)) is Relation-like Args (o,(C1)) -defined Result (o,(C1)) -valued Function-like V36( Args (o,(C1)), Result (o,(C1))) Element of bool [:(Args (o,(C1))),(Result (o,(C1))):]
Result (o,(C1)) is Element of proj2 the Sorts of (C1)
proj2 the Sorts of (C1) is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of (C1)) . o is set
[:(Args (o,(C1))),(Result (o,(C1))):] is Relation-like set
bool [:(Args (o,(C1))),(Result (o,(C1))):] is non empty set
the Charact of (C1) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of (C1) #), the ResultSort of ( the carrier of C1) * the Sorts of (C1)
the Charact of (C1) . o is Relation-like Function-like set
Den (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))) is Relation-like Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))) -defined Result (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))) -valued Function-like V36( Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))), Result (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))) Element of bool [:(Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))),(Result (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))):]
Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))) is Element of proj2 ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #)
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) # is Relation-like the carrier of ( the carrier of C1) * -defined Function-like non empty total set
proj2 ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #) is non empty set
the Arity of ( the carrier of C1) * ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the Arity of ( the carrier of C1) * ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #)) . o is set
Result (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))) is Element of proj2 the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))
proj2 the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) is non empty set
the ResultSort of ( the carrier of C1) * the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C1) * the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))) . o is set
[:(Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))),(Result (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))):] is Relation-like set
bool [:(Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))),(Result (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))):] is non empty set
the Charact of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) is Relation-like the carrier' of ( the carrier of C1) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C1) * ( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) #), the ResultSort of ( the carrier of C1) * the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F)))
the Charact of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . o is Relation-like Function-like set
o `1 is set
x is Element of the carrier of C1
( the carrier of C1,x) is Element of the carrier' of ( the carrier of C1)
<*x*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*x*>] is V21() set
{1,<*x*>} is non empty set
{{1,<*x*>},{1}} is non empty set
a is Element of Args (o,(C1))
(Den (o,(C1))) . a is set
(H . (the_result_sort_of o)) . ((Den (o,(C1))) . a) is set
H # a is Element of Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))
(Den (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))) . (H # a) is set
(C1,C2,F) . o is Element of the carrier' of ( the carrier of C2)
Args (((C1,C2,F) . o),(C2)) is Element of proj2 ( the Sorts of (C2) #)
the Sorts of (C2) is Relation-like the carrier of ( the carrier of C2) -defined Function-like non empty total V131() set
the Sorts of (C2) # is Relation-like the carrier of ( the carrier of C2) * -defined Function-like non empty total set
the carrier of ( the carrier of C2) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C2)
proj2 ( the Sorts of (C2) #) is non empty set
the Arity of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C2) -defined the carrier of ( the carrier of C2) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):]
[: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is non empty set
the Arity of ( the carrier of C2) * ( the Sorts of (C2) #) is Relation-like the carrier' of ( the carrier of C2) -defined Function-like non empty total set
( the Arity of ( the carrier of C2) * ( the Sorts of (C2) #)) . ((C1,C2,F) . o) is set
F . x is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . x is Element of the carrier of C2
( the carrier of C2,(F . x)) is Element of the carrier' of ( the carrier of C2)
<*(F . x)*> is Relation-like NAT -defined Function-like non empty V24() V31(1) FinSequence-like FinSubsequence-like set
[1,<*(F . x)*>] is V21() set
{1,<*(F . x)*>} is non empty set
{{1,<*(F . x)*>},{1}} is non empty set
id x is Morphism of x,x
dom (id x) is Element of the carrier of C1
cod (id x) is Element of the carrier of C1
Hom (x,x) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C1 : ( dom b<sub>1</sub> = x & cod b<sub>1</sub> = x ) } is set
b is Morphism of x,x
(H . (the_result_sort_of o)) . b is set
( the carrier of C1,x,x) is Element of the carrier of ( the carrier of C1)
<*x,x*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*x,x*>] is V21() set
{0,<*x,x*>} is functional non empty set
{{0,<*x,x*>},{0}} is non empty set
H . ( the carrier of C1,x,x) is Relation-like the Sorts of (C1) . ( the carrier of C1,x,x) -defined the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,x,x) -valued Function-like V36( the Sorts of (C1) . ( the carrier of C1,x,x), the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,x,x)) Element of bool [:( the Sorts of (C1) . ( the carrier of C1,x,x)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,x,x)):]
the Sorts of (C1) . ( the carrier of C1,x,x) is set
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,x,x) is set
[:( the Sorts of (C1) . ( the carrier of C1,x,x)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,x,x)):] is Relation-like set
bool [:( the Sorts of (C1) . ( the carrier of C1,x,x)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,x,x)):] is non empty set
(H . ( the carrier of C1,x,x)) . b is set
F | ( the Sorts of (C1) . ( the carrier of C1,x,x)) is Relation-like the carrier' of C1 -defined the Sorts of (C1) . ( the carrier of C1,x,x) -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
[: the carrier' of C1, the carrier' of C2:] is Relation-like non empty set
bool [: the carrier' of C1, the carrier' of C2:] is non empty set
(F | ( the Sorts of (C1) . ( the carrier of C1,x,x))) . b is set
F | (Hom (x,x)) is Relation-like the carrier' of C1 -defined Hom (x,x) -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
(F | (Hom (x,x))) . b is set
hom (F,x,x) is Relation-like Hom (x,x) -defined Hom ((F . x),(F . x)) -valued Function-like V36( Hom (x,x), Hom ((F . x),(F . x))) Element of bool [:(Hom (x,x)),(Hom ((F . x),(F . x))):]
Hom ((F . x),(F . x)) is Element of bool the carrier' of C2
bool the carrier' of C2 is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier' of C2 : ( dom b<sub>1</sub> = F . x & cod b<sub>1</sub> = F . x ) } is set
[:(Hom (x,x)),(Hom ((F . x),(F . x))):] is Relation-like set
bool [:(Hom (x,x)),(Hom ((F . x),(F . x))):] is non empty set
(hom (F,x,x)) . b is set
F . b is Element of the carrier' of C2
id (F . x) is Morphism of F . x,F . x
Den (((C1,C2,F) . o),(C2)) is Relation-like Args (((C1,C2,F) . o),(C2)) -defined Result (((C1,C2,F) . o),(C2)) -valued Function-like V36( Args (((C1,C2,F) . o),(C2)), Result (((C1,C2,F) . o),(C2))) Element of bool [:(Args (((C1,C2,F) . o),(C2))),(Result (((C1,C2,F) . o),(C2))):]
Result (((C1,C2,F) . o),(C2)) is Element of proj2 the Sorts of (C2)
proj2 the Sorts of (C2) is non empty set
the ResultSort of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C2) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):]
[: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):] is non empty set
the ResultSort of ( the carrier of C2) * the Sorts of (C2) is Relation-like the carrier' of ( the carrier of C2) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C2) * the Sorts of (C2)) . ((C1,C2,F) . o) is set
[:(Args (((C1,C2,F) . o),(C2))),(Result (((C1,C2,F) . o),(C2))):] is Relation-like set
bool [:(Args (((C1,C2,F) . o),(C2))),(Result (((C1,C2,F) . o),(C2))):] is non empty set
the Charact of (C2) is Relation-like the carrier' of ( the carrier of C2) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C2) * ( the Sorts of (C2) #), the ResultSort of ( the carrier of C2) * the Sorts of (C2)
the Charact of (C2) . ((C1,C2,F) . o) is Relation-like Function-like set
(Den (((C1,C2,F) . o),(C2))) . (H # a) is set
o `1 is set
x is Element of Args (o,(C1))
(Den (o,(C1))) . x is set
(H . (the_result_sort_of o)) . ((Den (o,(C1))) . x) is set
H # x is Element of Args (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))
(Den (o,((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))))) . (H # x) is set
a is Element of the carrier of C1
b is Element of the carrier of C1
c is Element of the carrier of C1
( the carrier of C1,a,b,c) is Element of the carrier' of ( the carrier of C1)
<*a,b,c*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*a,b,c*>] is V21() set
{2,<*a,b,c*>} is non empty set
{{2,<*a,b,c*>},{2}} is non empty set
(C1,C2,F) . o is Element of the carrier' of ( the carrier of C2)
F . a is Element of the carrier of C2
Obj F is Relation-like the carrier of C1 -defined the carrier of C2 -valued Function-like non empty total V36( the carrier of C1, the carrier of C2) Element of bool [: the carrier of C1, the carrier of C2:]
[: the carrier of C1, the carrier of C2:] is Relation-like non empty set
bool [: the carrier of C1, the carrier of C2:] is non empty set
(Obj F) . a is Element of the carrier of C2
F . b is Element of the carrier of C2
(Obj F) . b is Element of the carrier of C2
F . c is Element of the carrier of C2
(Obj F) . c is Element of the carrier of C2
( the carrier of C2,(F . a),(F . b),(F . c)) is Element of the carrier' of ( the carrier of C2)
<*(F . a),(F . b),(F . c)*> is Relation-like NAT -defined Function-like non empty V24() V31(3) FinSequence-like FinSubsequence-like set
[2,<*(F . a),(F . b),(F . c)*>] is V21() set
{2,<*(F . a),(F . b),(F . c)*>} is non empty set
{{2,<*(F . a),(F . b),(F . c)*>},{2}} is non empty set
g is Element of the carrier' of C1
h is Element of the carrier' of C1
<*g,h*> is Relation-like NAT -defined the carrier' of C1 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C1
dom h is Element of the carrier of C1
cod h is Element of the carrier of C1
dom g is Element of the carrier of C1
cod g is Element of the carrier of C1
Hom (b,c) is Element of bool the carrier' of C1
bool the carrier' of C1 is non empty set
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = b & cod b₁ = c ) } is set
Hom (a,b) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = a & cod b₁ = b ) } is set
g (*) h is Element of the carrier' of C1
dom (g (*) h) is Element of the carrier of C1
cod (g (*) h) is Element of the carrier of C1
Hom (a,c) is Element of bool the carrier' of C1
{ b₁ where b₁ is Element of the carrier' of C1 : ( dom b₁ = a & cod b₁ = c ) } is set
F . h is Element of the carrier' of C2
dom (F . h) is Element of the carrier of C2
cod (F . h) is Element of the carrier of C2
F . g is Element of the carrier' of C2
dom (F . g) is Element of the carrier of C2
cod (F . g) is Element of the carrier of C2
gh is Morphism of a,c
(H . (the_result_sort_of o)) . gh is set
( the carrier of C1,a,c) is Element of the carrier of ( the carrier of C1)
<*a,c*> is Relation-like NAT -defined Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like set
[0,<*a,c*>] is V21() set
{0,<*a,c*>} is functional non empty set
{{0,<*a,c*>},{0}} is non empty set
H . ( the carrier of C1,a,c) is Relation-like the Sorts of (C1) . ( the carrier of C1,a,c) -defined the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,a,c) -valued Function-like V36( the Sorts of (C1) . ( the carrier of C1,a,c), the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,a,c)) Element of bool [:( the Sorts of (C1) . ( the carrier of C1,a,c)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,a,c)):]
the Sorts of (C1) . ( the carrier of C1,a,c) is set
the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,a,c) is set
[:( the Sorts of (C1) . ( the carrier of C1,a,c)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,a,c)):] is Relation-like set
bool [:( the Sorts of (C1) . ( the carrier of C1,a,c)),( the Sorts of ((C2) | (( the carrier of C1),(C1,C2,F),(C1,C2,F))) . ( the carrier of C1,a,c)):] is non empty set
(H . ( the carrier of C1,a,c)) . gh is set
F | ( the Sorts of (C1) . ( the carrier of C1,a,c)) is Relation-like the carrier' of C1 -defined the Sorts of (C1) . ( the carrier of C1,a,c) -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
[: the carrier' of C1, the carrier' of C2:] is Relation-like non empty set
bool [: the carrier' of C1, the carrier' of C2:] is non empty set
(F | ( the Sorts of (C1) . ( the carrier of C1,a,c))) . gh is set
F | (Hom (a,c)) is Relation-like the carrier' of C1 -defined Hom (a,c) -defined the carrier' of C1 -defined the carrier' of C2 -valued Function-like Element of bool [: the carrier' of C1, the carrier' of C2:]
(F | (Hom (a,c))) . gh is set
hom (F,a,c) is Relation-like Hom (a,c) -defined Hom ((F . a),(F . c)) -valued Function-like V36( Hom (a,c), Hom ((F . a),(F . c))) Element of bool [:(Hom (a,c)),(Hom ((F . a),(F . c))):]
Hom ((F . a),(F . c)) is Element of bool the carrier' of C2
bool the carrier' of C2 is non empty set
{ b₁ where b₁ is Element of the carrier' of C2 : ( dom b₁ = F . a & cod b₁ = F . c ) } is set
[:(Hom (a,c)),(Hom ((F . a),(F . c))):] is Relation-like set
bool [:(Hom (a,c)),(Hom ((F . a),(F . c))):] is non empty set
(hom (F,a,c)) . gh is set
F . gh is Element of the carrier' of C2
(F . g) (*) (F . h) is Element of the carrier' of C2
Den (((C1,C2,F) . o),(C2)) is Relation-like Args (((C1,C2,F) . o),(C2)) -defined Result (((C1,C2,F) . o),(C2)) -valued Function-like V36( Args (((C1,C2,F) . o),(C2)), Result (((C1,C2,F) . o),(C2))) Element of bool [:(Args (((C1,C2,F) . o),(C2))),(Result (((C1,C2,F) . o),(C2))):]
Args (((C1,C2,F) . o),(C2)) is Element of proj2 ( the Sorts of (C2) #)
the Sorts of (C2) is Relation-like the carrier of ( the carrier of C2) -defined Function-like non empty total V131() set
the Sorts of (C2) # is Relation-like the carrier of ( the carrier of C2) * -defined Function-like non empty total set
the carrier of ( the carrier of C2) * is functional non empty FinSequence-membered FinSequenceSet of the carrier of ( the carrier of C2)
proj2 ( the Sorts of (C2) #) is non empty set
the Arity of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C2) -defined the carrier of ( the carrier of C2) * -valued Function-like non empty total V36( the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2) * ) Function-yielding V78() Element of bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):]
[: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C2),( the carrier of ( the carrier of C2) *):] is non empty set
the Arity of ( the carrier of C2) * ( the Sorts of (C2) #) is Relation-like the carrier' of ( the carrier of C2) -defined Function-like non empty total set
( the Arity of ( the carrier of C2) * ( the Sorts of (C2) #)) . ((C1,C2,F) . o) is set
Result (((C1,C2,F) . o),(C2)) is Element of proj2 the Sorts of (C2)
proj2 the Sorts of (C2) is non empty set
the ResultSort of ( the carrier of C2) is Relation-like the carrier' of ( the carrier of C2) -defined the carrier of ( the carrier of C2) -valued Function-like non empty total V36( the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2)) Element of bool [: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):]
[: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):] is Relation-like non empty set
bool [: the carrier' of ( the carrier of C2), the carrier of ( the carrier of C2):] is non empty set
the ResultSort of ( the carrier of C2) * the Sorts of (C2) is Relation-like the carrier' of ( the carrier of C2) -defined Function-like non empty total set
( the ResultSort of ( the carrier of C2) * the Sorts of (C2)) . ((C1,C2,F) . o) is set
[:(Args (((C1,C2,F) . o),(C2))),(Result (((C1,C2,F) . o),(C2))):] is Relation-like set
bool [:(Args (((C1,C2,F) . o),(C2))),(Result (((C1,C2,F) . o),(C2))):] is non empty set
the Charact of (C2) is Relation-like the carrier' of ( the carrier of C2) -defined Function-like non empty total Function-yielding V78() ManySortedFunction of the Arity of ( the carrier of C2) * ( the Sorts of (C2) #), the ResultSort of ( the carrier of C2) * the Sorts of (C2)
the Charact of (C2) . ((C1,C2,F) . o) is Relation-like Function-like set
<*(F . g),(F . h)*> is Relation-like NAT -defined the carrier' of C2 -valued Function-like non empty V24() V31(2) FinSequence-like FinSubsequence-like FinSequence of the carrier' of C2
(Den (((C1,C2,F) . o),(C2))) . <*(F . g),(F . h)*> is set
(Den (((C1,C2,F) . o),(C2))) . (H # x) is set
o `1 is set