:: BVFUNC14 semantic presentation

K129() is Element of bool K125()
K125() is set
bool K125() is non empty set
K124() is set
bool K124() is non empty set
bool K129() is non empty set
K211() is set
{} is empty set
{{}} is non empty set
Y is non empty set
G is Element of Y
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
EqClass (G,(A '/\' B)) is Element of A '/\' B
EqClass (G,A) is Element of A
EqClass (G,B) is Element of B
(EqClass (G,A)) /\ (EqClass (G,B)) is Element of bool Y
bool Y is non empty set
D is set
E is Element of Y
EqClass (E,A) is Element of A
EqClass (E,B) is Element of B
INTERSECTION (A,B) is set
(INTERSECTION (A,B)) \ {{}} is Element of bool (INTERSECTION (A,B))
bool (INTERSECTION (A,B)) is non empty set
F is set
J is set
F /\ J is set
(EqClass (E,A)) /\ (EqClass (E,B)) is Element of bool Y
C is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
'/\' G is non empty with_non-empty_elements a_partition of Y
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is set
INTERSECTION (A,B) is set
(INTERSECTION (A,B)) \ {{}} is Element of bool (INTERSECTION (A,B))
bool (INTERSECTION (A,B)) is non empty set
D is set
E is set
D /\ E is set
(A,B) --> (D,E) is Relation-like bool (bool Y) -defined Function-like set
rng ((A,B) --> (D,E)) is set
{D,E} is non empty set
J is set
J is Element of bool (bool Y)
Intersect J is Element of bool Y
M is set
N is set
meet J is Element of bool Y
M is set
((A,B) --> (D,E)) . M is set
M is set
meet J is Element of bool Y
dom ((A,B) --> (D,E)) is set
C is set
D is Relation-like Function-like set
dom D is set
rng D is set
E is Element of bool (bool Y)
Intersect E is Element of bool Y
D . A is set
D . B is set
(D . A) /\ (D . B) is set
F is set
{(D . A),(D . B)} is non empty set
J is set
M is set
D . M is set
J is set
meet (rng D) is set
F is set
meet (rng D) is set
INTERSECTION (A,B) is set
(INTERSECTION (A,B)) \ {{}} is Element of bool (INTERSECTION (A,B))
bool (INTERSECTION (A,B)) is non empty set
Y is set
B is set
Y .--> B is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> B is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{B}) Element of bool [:{Y},{B}:]
{B} is non empty set
[:{Y},{B}:] is non empty set
bool [:{Y},{B}:] is non empty set
G is set
C is set
G .--> C is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> C is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{C}) Element of bool [:{G},{C}:]
{C} is non empty set
[:{G},{C}:] is non empty set
bool [:{G},{C}:] is non empty set
(Y .--> B) +* (G .--> C) is Relation-like Function-like set
A is set
D is set
A .--> D is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> D is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{D}) Element of bool [:{A},{D}:]
{D} is non empty set
[:{A},{D}:] is non empty set
bool [:{A},{D}:] is non empty set
((Y .--> B) +* (G .--> C)) +* (A .--> D) is Relation-like Function-like set
dom (((Y .--> B) +* (G .--> C)) +* (A .--> D)) is set
{Y,G,A} is non empty set
dom (G .--> C) is set
dom (A .--> D) is set
dom ((Y .--> B) +* (G .--> C)) is set
dom (Y .--> B) is set
(dom (Y .--> B)) \/ (dom (G .--> C)) is set
{Y} \/ {G} is non empty set
({Y} \/ {G}) \/ {A} is non empty set
{Y,G} is non empty set
{Y,G} \/ {A} is non empty set
Y is Relation-like Function-like set
G is set
A is set
B is set
G .--> B is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> B is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{B}) Element of bool [:{G},{B}:]
{B} is non empty set
[:{G},{B}:] is non empty set
bool [:{G},{B}:] is non empty set
Y +* (G .--> B) is Relation-like Function-like set
C is set
A .--> C is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> C is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{C}) Element of bool [:{A},{C}:]
{C} is non empty set
[:{A},{C}:] is non empty set
bool [:{A},{C}:] is non empty set
(Y +* (G .--> B)) +* (A .--> C) is Relation-like Function-like set
((Y +* (G .--> B)) +* (A .--> C)) . G is set
dom (A .--> C) is set
(Y +* (G .--> B)) . G is set
dom (G .--> B) is set
(G .--> B) . G is set
Y is set
G is set
A is set
B is set
Y .--> B is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> B is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{B}) Element of bool [:{Y},{B}:]
{B} is non empty set
[:{Y},{B}:] is non empty set
bool [:{Y},{B}:] is non empty set
C is set
G .--> C is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> C is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{C}) Element of bool [:{G},{C}:]
{C} is non empty set
[:{G},{C}:] is non empty set
bool [:{G},{C}:] is non empty set
(Y .--> B) +* (G .--> C) is Relation-like Function-like set
D is set
A .--> D is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> D is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{D}) Element of bool [:{A},{D}:]
{D} is non empty set
[:{A},{D}:] is non empty set
bool [:{A},{D}:] is non empty set
((Y .--> B) +* (G .--> C)) +* (A .--> D) is Relation-like Function-like set
(((Y .--> B) +* (G .--> C)) +* (A .--> D)) . Y is set
dom (A .--> D) is set
((Y .--> B) +* (G .--> C)) . Y is set
dom (G .--> C) is set
(Y .--> B) . Y is set
Y is set
B is set
Y .--> B is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> B is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{B}) Element of bool [:{Y},{B}:]
{B} is non empty set
[:{Y},{B}:] is non empty set
bool [:{Y},{B}:] is non empty set
G is set
C is set
G .--> C is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> C is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{C}) Element of bool [:{G},{C}:]
{C} is non empty set
[:{G},{C}:] is non empty set
bool [:{G},{C}:] is non empty set
(Y .--> B) +* (G .--> C) is Relation-like Function-like set
A is set
D is set
A .--> D is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> D is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{D}) Element of bool [:{A},{D}:]
{D} is non empty set
[:{A},{D}:] is non empty set
bool [:{A},{D}:] is non empty set
((Y .--> B) +* (G .--> C)) +* (A .--> D) is Relation-like Function-like set
E is Relation-like Function-like set
rng E is set
E . Y is set
E . G is set
E . A is set
{(E . Y),(E . G),(E . A)} is non empty set
dom E is set
{Y,G,A} is non empty set
F is set
J is set
E . J is set
F is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
'/\' G is non empty with_non-empty_elements a_partition of Y
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is set
INTERSECTION ((A '/\' B),C) is set
(INTERSECTION ((A '/\' B),C)) \ {{}} is Element of bool (INTERSECTION ((A '/\' B),C))
bool (INTERSECTION ((A '/\' B),C)) is non empty set
E is set
F is set
E /\ F is set
INTERSECTION (A,B) is set
(INTERSECTION (A,B)) \ {{}} is Element of bool (INTERSECTION (A,B))
bool (INTERSECTION (A,B)) is non empty set
J is set
M is set
J /\ M is set
A .--> J is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> J is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{J}) Element of bool [:{A},{J}:]
{J} is non empty set
[:{A},{J}:] is non empty set
bool [:{A},{J}:] is non empty set
B .--> M is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> M is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{M}) Element of bool [:{B},{M}:]
{M} is non empty set
[:{B},{M}:] is non empty set
bool [:{B},{M}:] is non empty set
(A .--> J) +* (B .--> M) is Relation-like bool (bool Y) -defined Function-like set
C .--> F is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> F is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{F}) Element of bool [:{C},{F}:]
{F} is non empty set
[:{C},{F}:] is non empty set
bool [:{C},{F}:] is non empty set
((A .--> J) +* (B .--> M)) +* (C .--> F) is Relation-like bool (bool Y) -defined Function-like set
rng (((A .--> J) +* (B .--> M)) +* (C .--> F)) is set
(((A .--> J) +* (B .--> M)) +* (C .--> F)) . A is set
(((A .--> J) +* (B .--> M)) +* (C .--> F)) . B is set
(((A .--> J) +* (B .--> M)) +* (C .--> F)) . C is set
{((((A .--> J) +* (B .--> M)) +* (C .--> F)) . A),((((A .--> J) +* (B .--> M)) +* (C .--> F)) . B),((((A .--> J) +* (B .--> M)) +* (C .--> F)) . C)} is non empty set
{((((A .--> J) +* (B .--> M)) +* (C .--> F)) . C),((((A .--> J) +* (B .--> M)) +* (C .--> F)) . A),((((A .--> J) +* (B .--> M)) +* (C .--> F)) . B)} is non empty set
z is set
u is set
(((A .--> J) +* (B .--> M)) +* (C .--> F)) . u is set
z is Element of bool (bool Y)
Intersect z is Element of bool Y
u is set
h is set
M /\ F is set
J /\ (M /\ F) is set
J /\ F is set
M /\ (J /\ F) is set
meet z is Element of bool Y
dom (((A .--> J) +* (B .--> M)) +* (C .--> F)) is set
u is set
meet (rng (((A .--> J) +* (B .--> M)) +* (C .--> F))) is set
D is set
E is Relation-like Function-like set
dom E is set
rng E is set
F is Element of bool (bool Y)
Intersect F is Element of bool Y
E . C is set
E . A is set
E . B is set
(E . A) /\ (E . B) is set
((E . A) /\ (E . B)) /\ (E . C) is set
M is set
meet (rng E) is set
INTERSECTION (A,B) is set
(INTERSECTION (A,B)) \ {{}} is Element of bool (INTERSECTION (A,B))
bool (INTERSECTION (A,B)) is non empty set
M is set
{(E . A),(E . B),(E . C)} is non empty set
N is set
z is set
E . z is set
N is set
meet (rng E) is set
INTERSECTION ((A '/\' B),C) is set
(INTERSECTION ((A '/\' B),C)) \ {{}} is Element of bool (INTERSECTION ((A '/\' B),C))
bool (INTERSECTION ((A '/\' B),C)) is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
B '/\' C is non empty with_non-empty_elements a_partition of Y
{B,C,A} is non empty set
{B,A} is non empty set
{A} is non empty Element of bool (PARTITIONS Y)
G \ {A} is Element of bool (PARTITIONS Y)
{B,C} is non empty set
{A} \/ {B,C} is non empty set
({A} \/ {B,C}) \ {A} is Element of bool ({A} \/ {B,C})
bool ({A} \/ {B,C}) is non empty set
{A} \ {A} is Element of bool (PARTITIONS Y)
{B,C} \ {A} is Element of bool {B,C}
bool {B,C} is non empty set
({A} \ {A}) \/ ({B,C} \ {A}) is set
({A} \ {A}) \/ {B,C} is non empty set
{} \/ {B,C} is non empty set
'/\' (G \ {A}) is non empty with_non-empty_elements a_partition of Y
D is set
E is Relation-like Function-like set
dom E is set
rng E is set
F is Element of bool (bool Y)
Intersect F is Element of bool Y
E . B is set
E . C is set
(E . B) /\ (E . C) is set
J is set
{(E . B),(E . C)} is non empty set
M is set
N is set
E . N is set
M is set
meet (rng E) is set
J is set
meet (rng E) is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
D is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
E is set
F is set
E /\ F is set
(B,C) --> (E,F) is Relation-like bool (bool Y) -defined Function-like set
dom ((B,C) --> (E,F)) is set
rng ((B,C) --> (E,F)) is set
{E,F} is non empty set
M is set
M is Element of bool (bool Y)
Intersect M is Element of bool Y
N is set
z is set
meet M is Element of bool Y
N is set
((B,C) --> (E,F)) . N is set
N is set
meet M is Element of bool Y
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
C '/\' A is non empty with_non-empty_elements a_partition of Y
{B,C,A} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
CompF (C,G) is non empty with_non-empty_elements a_partition of Y
{C,A,B} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
{B,B,A,D} is non empty set
{B,A,D} is non empty set
{A,B,D} is non empty set
B '/\' D is non empty with_non-empty_elements a_partition of Y
{B,B,A,C} is non empty set
{B,A,C} is non empty set
{A,B,C} is non empty set
B '/\' D is non empty with_non-empty_elements a_partition of Y
(B '/\' D) '/\' C is non empty with_non-empty_elements a_partition of Y
{C,C,A,B} is non empty set
{C,A,B} is non empty set
{A,B,C} is non empty set
C '/\' D is non empty with_non-empty_elements a_partition of Y
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
G \ {A} is Element of bool (PARTITIONS Y)
{B,C,D} is non empty set
{A} \/ {B,C,D} is non empty set
({A} \/ {B,C,D}) \ {A} is Element of bool ({A} \/ {B,C,D})
bool ({A} \/ {B,C,D}) is non empty set
{A} \ {A} is Element of bool (PARTITIONS Y)
{B,C,D} \ {A} is Element of bool {B,C,D}
bool {B,C,D} is non empty set
({A} \ {A}) \/ ({B,C,D} \ {A}) is set
{B} is non empty Element of bool (PARTITIONS Y)
{C,D} is non empty set
{B} \/ {C,D} is non empty set
({B} \/ {C,D}) \ {A} is Element of bool ({B} \/ {C,D})
bool ({B} \/ {C,D}) is non empty set
{B} \ {A} is Element of bool (PARTITIONS Y)
{C,D} \ {A} is Element of bool {C,D}
bool {C,D} is non empty set
({B} \ {A}) \/ ({C,D} \ {A}) is set
({B} \ {A}) \/ {C,D} is non empty set
{} \/ {B,C,D} is non empty set
'/\' (G \ {A}) is non empty with_non-empty_elements a_partition of Y
E is set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
F is set
J is set
F /\ J is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
M is set
N is set
M /\ N is set
B .--> M is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> M is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{M}) Element of bool [:{B},{M}:]
{M} is non empty set
[:{B},{M}:] is non empty set
bool [:{B},{M}:] is non empty set
C .--> N is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> N is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{N}) Element of bool [:{C},{N}:]
{N} is non empty set
[:{C},{N}:] is non empty set
bool [:{C},{N}:] is non empty set
(B .--> M) +* (C .--> N) is Relation-like bool (bool Y) -defined Function-like set
D .--> J is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> J is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{J}) Element of bool [:{D},{J}:]
{J} is non empty set
[:{D},{J}:] is non empty set
bool [:{D},{J}:] is non empty set
((B .--> M) +* (C .--> N)) +* (D .--> J) is Relation-like bool (bool Y) -defined Function-like set
(((B .--> M) +* (C .--> N)) +* (D .--> J)) . D is set
(((B .--> M) +* (C .--> N)) +* (D .--> J)) . C is set
rng (((B .--> M) +* (C .--> N)) +* (D .--> J)) is set
(((B .--> M) +* (C .--> N)) +* (D .--> J)) . B is set
{((((B .--> M) +* (C .--> N)) +* (D .--> J)) . B),((((B .--> M) +* (C .--> N)) +* (D .--> J)) . C),((((B .--> M) +* (C .--> N)) +* (D .--> J)) . D)} is non empty set
{((((B .--> M) +* (C .--> N)) +* (D .--> J)) . D),((((B .--> M) +* (C .--> N)) +* (D .--> J)) . B),((((B .--> M) +* (C .--> N)) +* (D .--> J)) . C)} is non empty set
u is set
u is Element of bool (bool Y)
Intersect u is Element of bool Y
h is set
L is set
N /\ J is set
M /\ (N /\ J) is set
M /\ J is set
N /\ (M /\ J) is set
meet u is Element of bool Y
h is set
(((B .--> M) +* (C .--> N)) +* (D .--> J)) . h is set
dom (((B .--> M) +* (C .--> N)) +* (D .--> J)) is set
h is set
meet (rng (((B .--> M) +* (C .--> N)) +* (D .--> J))) is set
E is set
F is Relation-like Function-like set
dom F is set
rng F is set
J is Element of bool (bool Y)
Intersect J is Element of bool Y
F . D is set
F . B is set
F . C is set
(F . B) /\ (F . C) is set
((F . B) /\ (F . C)) /\ (F . D) is set
N is set
meet (rng F) is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
N is set
{(F . B),(F . C),(F . D)} is non empty set
z is set
u is set
F . u is set
z is set
meet (rng F) is set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
{B,A,C,D} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
CompF (C,G) is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
(A '/\' B) '/\' D is non empty with_non-empty_elements a_partition of Y
{C,A,B,D} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' B is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
CompF (D,G) is non empty with_non-empty_elements a_partition of Y
{D,A,C,B} is non empty set
Y is set
B is set
Y .--> B is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> B is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{B}) Element of bool [:{Y},{B}:]
{B} is non empty set
[:{Y},{B}:] is non empty set
bool [:{Y},{B}:] is non empty set
G is set
C is set
G .--> C is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> C is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{C}) Element of bool [:{G},{C}:]
{C} is non empty set
[:{G},{C}:] is non empty set
bool [:{G},{C}:] is non empty set
(Y .--> B) +* (G .--> C) is Relation-like Function-like set
A is set
D is set
A .--> D is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> D is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{D}) Element of bool [:{A},{D}:]
{D} is non empty set
[:{A},{D}:] is non empty set
bool [:{A},{D}:] is non empty set
((Y .--> B) +* (G .--> C)) +* (A .--> D) is Relation-like Function-like set
dom (((Y .--> B) +* (G .--> C)) +* (A .--> D)) is set
{Y,G,A} is non empty set
G is set
A is set
Y is Relation-like Function-like set
B is set
G .--> B is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> B is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{B}) Element of bool [:{G},{B}:]
{B} is non empty set
[:{G},{B}:] is non empty set
bool [:{G},{B}:] is non empty set
Y +* (G .--> B) is Relation-like Function-like set
C is set
A .--> C is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> C is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{C}) Element of bool [:{A},{C}:]
{C} is non empty set
[:{A},{C}:] is non empty set
bool [:{A},{C}:] is non empty set
(Y +* (G .--> B)) +* (A .--> C) is Relation-like Function-like set
((Y +* (G .--> B)) +* (A .--> C)) . G is set
Y is set
G is set
A is set
B is set
Y .--> B is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> B is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{B}) Element of bool [:{Y},{B}:]
{B} is non empty set
[:{Y},{B}:] is non empty set
bool [:{Y},{B}:] is non empty set
C is set
G .--> C is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> C is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{C}) Element of bool [:{G},{C}:]
{C} is non empty set
[:{G},{C}:] is non empty set
bool [:{G},{C}:] is non empty set
(Y .--> B) +* (G .--> C) is Relation-like Function-like set
D is set
A .--> D is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> D is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{D}) Element of bool [:{A},{D}:]
{D} is non empty set
[:{A},{D}:] is non empty set
bool [:{A},{D}:] is non empty set
((Y .--> B) +* (G .--> C)) +* (A .--> D) is Relation-like Function-like set
(((Y .--> B) +* (G .--> C)) +* (A .--> D)) . Y is set
E is Relation-like Function-like set
Y is set
B is set
Y .--> B is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> B is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{B}) Element of bool [:{Y},{B}:]
{B} is non empty set
[:{Y},{B}:] is non empty set
bool [:{Y},{B}:] is non empty set
G is set
C is set
G .--> C is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> C is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{C}) Element of bool [:{G},{C}:]
{C} is non empty set
[:{G},{C}:] is non empty set
bool [:{G},{C}:] is non empty set
(Y .--> B) +* (G .--> C) is Relation-like Function-like set
A is set
D is set
A .--> D is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> D is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{D}) Element of bool [:{A},{D}:]
{D} is non empty set
[:{A},{D}:] is non empty set
bool [:{A},{D}:] is non empty set
((Y .--> B) +* (G .--> C)) +* (A .--> D) is Relation-like Function-like set
rng E is set
E . Y is set
E . G is set
E . A is set
{(E . Y),(E . G),(E . A)} is non empty set
Y is non empty set
G is non empty with_non-empty_elements a_partition of Y
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is Relation-like Function-like set
D . A is set
D . B is set
D . C is set
F is set
A .--> F is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined Function-like one-to-one set
{A} is non empty set
bool Y is non empty set
bool (bool Y) is non empty set
{A} --> F is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{F}) Element of bool [:{A},{F}:]
{F} is non empty set
[:{A},{F}:] is non empty set
bool [:{A},{F}:] is non empty set
J is set
B .--> J is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> J is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{J}) Element of bool [:{B},{J}:]
{J} is non empty set
[:{B},{J}:] is non empty set
bool [:{B},{J}:] is non empty set
(A .--> F) +* (B .--> J) is Relation-like bool (bool Y) -defined Function-like set
M is set
C .--> M is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> M is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{M}) Element of bool [:{C},{M}:]
{M} is non empty set
[:{C},{M}:] is non empty set
bool [:{C},{M}:] is non empty set
((A .--> F) +* (B .--> J)) +* (C .--> M) is Relation-like bool (bool Y) -defined Function-like set
E is set
G .--> E is trivial Relation-like {G} -defined bool (bool Y) -defined {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> E is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{E}) Element of bool [:{G},{E}:]
{E} is non empty set
[:{G},{E}:] is non empty set
bool [:{G},{E}:] is non empty set
(((A .--> F) +* (B .--> J)) +* (C .--> M)) +* (G .--> E) is Relation-like bool (bool Y) -defined Function-like set
dom (G .--> E) is set
{G} is non empty Element of bool (PARTITIONS Y)
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
(((A .--> F) +* (B .--> J)) +* (C .--> M)) . C is set
(((A .--> F) +* (B .--> J)) +* (C .--> M)) . B is set
dom (C .--> M) is set
{C} is non empty Element of bool (PARTITIONS Y)
((A .--> F) +* (B .--> J)) . B is set
(((A .--> F) +* (B .--> J)) +* (C .--> M)) . A is set
((A .--> F) +* (B .--> J)) . A is set
dom (B .--> J) is set
{B} is non empty Element of bool (PARTITIONS Y)
(A .--> F) . A is set
(B .--> J) . B is set
(C .--> M) . C is set
G is set
A is set
B is set
Y is set
{Y,G,A,B} is non empty set
C is Relation-like Function-like set
dom C is set
E is set
G .--> E is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> E is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{E}) Element of bool [:{G},{E}:]
{E} is non empty set
[:{G},{E}:] is non empty set
bool [:{G},{E}:] is non empty set
F is set
A .--> F is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> F is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{F}) Element of bool [:{A},{F}:]
{F} is non empty set
[:{A},{F}:] is non empty set
bool [:{A},{F}:] is non empty set
(G .--> E) +* (A .--> F) is Relation-like Function-like set
J is set
B .--> J is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> J is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{J}) Element of bool [:{B},{J}:]
{J} is non empty set
[:{B},{J}:] is non empty set
bool [:{B},{J}:] is non empty set
((G .--> E) +* (A .--> F)) +* (B .--> J) is Relation-like Function-like set
D is set
Y .--> D is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> D is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{D}) Element of bool [:{Y},{D}:]
{D} is non empty set
[:{Y},{D}:] is non empty set
bool [:{Y},{D}:] is non empty set
(((G .--> E) +* (A .--> F)) +* (B .--> J)) +* (Y .--> D) is Relation-like Function-like set
dom ((G .--> E) +* (A .--> F)) is set
dom (G .--> E) is set
dom (A .--> F) is set
(dom (G .--> E)) \/ (dom (A .--> F)) is set
dom (((G .--> E) +* (A .--> F)) +* (B .--> J)) is set
dom (B .--> J) is set
((dom (G .--> E)) \/ (dom (A .--> F))) \/ (dom (B .--> J)) is set
dom ((((G .--> E) +* (A .--> F)) +* (B .--> J)) +* (Y .--> D)) is set
{G} \/ (dom (A .--> F)) is non empty set
({G} \/ (dom (A .--> F))) \/ (dom (B .--> J)) is non empty set
dom (Y .--> D) is set
(({G} \/ (dom (A .--> F))) \/ (dom (B .--> J))) \/ (dom (Y .--> D)) is non empty set
{G} \/ {A} is non empty set
({G} \/ {A}) \/ (dom (B .--> J)) is non empty set
(({G} \/ {A}) \/ (dom (B .--> J))) \/ (dom (Y .--> D)) is non empty set
({G} \/ {A}) \/ {B} is non empty set
(({G} \/ {A}) \/ {B}) \/ (dom (Y .--> D)) is non empty set
{Y} \/ (({G} \/ {A}) \/ {B}) is non empty set
{G,A} is non empty set
{G,A} \/ {B} is non empty set
{Y} \/ ({G,A} \/ {B}) is non empty set
{G,A,B} is non empty set
{Y} \/ {G,A,B} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
E is Relation-like Function-like set
rng E is set
E . A is set
E . B is set
E . C is set
E . D is set
{(E . A),(E . B),(E . C),(E . D)} is non empty set
J is set
B .--> J is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> J is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{J}) Element of bool [:{B},{J}:]
{J} is non empty set
[:{B},{J}:] is non empty set
bool [:{B},{J}:] is non empty set
M is set
C .--> M is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> M is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{M}) Element of bool [:{C},{M}:]
{M} is non empty set
[:{C},{M}:] is non empty set
bool [:{C},{M}:] is non empty set
(B .--> J) +* (C .--> M) is Relation-like bool (bool Y) -defined Function-like set
N is set
D .--> N is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> N is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{N}) Element of bool [:{D},{N}:]
{N} is non empty set
[:{D},{N}:] is non empty set
bool [:{D},{N}:] is non empty set
((B .--> J) +* (C .--> M)) +* (D .--> N) is Relation-like bool (bool Y) -defined Function-like set
F is set
A .--> F is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> F is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{F}) Element of bool [:{A},{F}:]
{F} is non empty set
[:{A},{F}:] is non empty set
bool [:{A},{F}:] is non empty set
(((B .--> J) +* (C .--> M)) +* (D .--> N)) +* (A .--> F) is Relation-like bool (bool Y) -defined Function-like set
dom E is set
z is set
u is set
E . u is set
z is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
F is Element of Y
EqClass (F,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
E is Element of Y
EqClass (E,A) is Element of A
EqClass (F,B) is Element of B
B .--> (EqClass (F,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (F,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (F,B))}) Element of bool [:{B},{(EqClass (F,B))}:]
{(EqClass (F,B))} is non empty set
[:{B},{(EqClass (F,B))}:] is non empty set
bool [:{B},{(EqClass (F,B))}:] is non empty set
EqClass (F,C) is Element of C
C .--> (EqClass (F,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (F,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (F,C))}) Element of bool [:{C},{(EqClass (F,C))}:]
{(EqClass (F,C))} is non empty set
[:{C},{(EqClass (F,C))}:] is non empty set
bool [:{C},{(EqClass (F,C))}:] is non empty set
(B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (F,D) is Element of D
D .--> (EqClass (F,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (F,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (F,D))}) Element of bool [:{D},{(EqClass (F,D))}:]
{(EqClass (F,D))} is non empty set
[:{D},{(EqClass (F,D))}:] is non empty set
bool [:{D},{(EqClass (F,D))}:] is non empty set
((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D))) is Relation-like bool (bool Y) -defined Function-like set
A .--> (EqClass (E,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (E,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (E,A))}) Element of bool [:{A},{(EqClass (E,A))}:]
{(EqClass (E,A))} is non empty set
[:{A},{(EqClass (E,A))}:] is non empty set
bool [:{A},{(EqClass (E,A))}:] is non empty set
(((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A))) is Relation-like bool (bool Y) -defined Function-like set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . B is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . D is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . C is set
rng ((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . A is set
{(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . A),(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . B),(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . C),(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . D)} is non empty set
N is set
dom ((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) is set
z is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . z is set
N is Element of bool (bool Y)
Intersect N is Element of bool Y
z is set
meet N is Element of bool Y
(EqClass (F,B)) /\ (EqClass (F,C)) is Element of bool Y
((EqClass (F,B)) /\ (EqClass (F,C))) /\ (EqClass (F,D)) is Element of bool Y
(((EqClass (F,B)) /\ (EqClass (F,C))) /\ (EqClass (F,D))) /\ (EqClass (E,A)) is Element of bool Y
EqClass (F,(B '/\' C)) is Element of B '/\' C
(EqClass (F,(B '/\' C))) /\ (EqClass (F,D)) is Element of bool Y
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
C '/\' D is non empty with_non-empty_elements a_partition of Y
E is Element of Y
EqClass (E,(C '/\' D)) is Element of C '/\' D
F is Element of Y
EqClass (F,(C '/\' D)) is Element of C '/\' D
EqClass (F,(CompF (A,G))) is Element of CompF (A,G)
EqClass (E,(CompF (B,G))) is Element of CompF (B,G)
EqClass (F,B) is Element of B
B .--> (EqClass (F,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (F,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (F,B))}) Element of bool [:{B},{(EqClass (F,B))}:]
{(EqClass (F,B))} is non empty set
[:{B},{(EqClass (F,B))}:] is non empty set
bool [:{B},{(EqClass (F,B))}:] is non empty set
EqClass (F,C) is Element of C
C .--> (EqClass (F,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (F,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (F,C))}) Element of bool [:{C},{(EqClass (F,C))}:]
{(EqClass (F,C))} is non empty set
[:{C},{(EqClass (F,C))}:] is non empty set
bool [:{C},{(EqClass (F,C))}:] is non empty set
(B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (F,D) is Element of D
D .--> (EqClass (F,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (F,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (F,D))}) Element of bool [:{D},{(EqClass (F,D))}:]
{(EqClass (F,D))} is non empty set
[:{D},{(EqClass (F,D))}:] is non empty set
bool [:{D},{(EqClass (F,D))}:] is non empty set
((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (E,A) is Element of A
A .--> (EqClass (E,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (E,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (E,A))}) Element of bool [:{A},{(EqClass (E,A))}:]
{(EqClass (E,A))} is non empty set
[:{A},{(EqClass (E,A))}:] is non empty set
bool [:{A},{(EqClass (E,A))}:] is non empty set
(((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A))) is Relation-like bool (bool Y) -defined Function-like set
A '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
rng ((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . A is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . B is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . C is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . D is set
{(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . A),(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . B),(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . C),(((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . D)} is non empty set
N is set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
EqClass (F,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
EqClass (F,(B '/\' C)) is Element of B '/\' C
(EqClass (F,(B '/\' C))) /\ (EqClass (F,D)) is Element of bool Y
h is set
((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) . h is set
dom ((((B .--> (EqClass (F,B))) +* (C .--> (EqClass (F,C)))) +* (D .--> (EqClass (F,D)))) +* (A .--> (EqClass (E,A)))) is set
N is Element of bool (bool Y)
Intersect N is Element of bool Y
h is set
meet N is Element of bool Y
(EqClass (F,B)) /\ (EqClass (F,C)) is Element of bool Y
((EqClass (F,B)) /\ (EqClass (F,C))) /\ (EqClass (F,D)) is Element of bool Y
(((EqClass (F,B)) /\ (EqClass (F,C))) /\ (EqClass (F,D))) /\ (EqClass (E,A)) is Element of bool Y
(EqClass (F,((B '/\' C) '/\' D))) /\ (EqClass (E,A)) is Element of bool Y
L is set
GG is Element of Y
EqClass (GG,(C '/\' D)) is Element of C '/\' D
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
EqClass (F,(B '/\' (C '/\' D))) is Element of B '/\' (C '/\' D)
(EqClass (E,A)) /\ (EqClass (GG,(C '/\' D))) is Element of bool Y
INTERSECTION (A,(C '/\' D)) is set
(INTERSECTION (A,(C '/\' D))) \ {{}} is Element of bool (INTERSECTION (A,(C '/\' D)))
bool (INTERSECTION (A,(C '/\' D))) is non empty set
(EqClass (F,((B '/\' C) '/\' D))) /\ (EqClass (E,(CompF (B,G)))) is Element of bool Y
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
D is Element of Y
EqClass (D,C) is Element of C
E is Element of Y
EqClass (E,C) is Element of C
EqClass (E,(CompF (A,G))) is Element of CompF (A,G)
EqClass (D,(CompF (B,G))) is Element of CompF (B,G)
EqClass (E,B) is Element of B
B .--> (EqClass (E,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (E,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (E,B))}) Element of bool [:{B},{(EqClass (E,B))}:]
{(EqClass (E,B))} is non empty set
[:{B},{(EqClass (E,B))}:] is non empty set
bool [:{B},{(EqClass (E,B))}:] is non empty set
C .--> (EqClass (E,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (E,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (E,C))}) Element of bool [:{C},{(EqClass (E,C))}:]
{(EqClass (E,C))} is non empty set
[:{C},{(EqClass (E,C))}:] is non empty set
bool [:{C},{(EqClass (E,C))}:] is non empty set
(B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (D,A) is Element of A
A .--> (EqClass (D,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (D,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (D,A))}) Element of bool [:{A},{(EqClass (D,A))}:]
{(EqClass (D,A))} is non empty set
[:{A},{(EqClass (D,A))}:] is non empty set
bool [:{A},{(EqClass (D,A))}:] is non empty set
((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A))) is Relation-like bool (bool Y) -defined Function-like set
dom (A .--> (EqClass (D,A))) is set
{A} is non empty Element of bool (PARTITIONS Y)
(((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . A is set
(A .--> (EqClass (D,A))) . A is set
B '/\' C is non empty with_non-empty_elements a_partition of Y
EqClass (E,(B '/\' C)) is Element of B '/\' C
(EqClass (E,(B '/\' C))) /\ (EqClass (D,A)) is Element of bool Y
(EqClass (E,B)) /\ (EqClass (E,C)) is Element of bool Y
((EqClass (E,B)) /\ (EqClass (E,C))) /\ (EqClass (D,A)) is Element of bool Y
dom ((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) is set
dom (B .--> (EqClass (E,B))) is set
dom (C .--> (EqClass (E,C))) is set
(dom (B .--> (EqClass (E,B)))) \/ (dom (C .--> (EqClass (E,C)))) is set
dom (((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) is set
((dom (B .--> (EqClass (E,B)))) \/ (dom (C .--> (EqClass (E,C))))) \/ (dom (A .--> (EqClass (D,A)))) is set
{C} is non empty Element of bool (PARTITIONS Y)
(((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . B is set
((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) . B is set
(B .--> (EqClass (E,B))) . B is set
(((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . C is set
((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) . C is set
(C .--> (EqClass (E,C))) . C is set
{B} is non empty Element of bool (PARTITIONS Y)
{A} \/ {B} is non empty Element of bool (PARTITIONS Y)
({A} \/ {B}) \/ {C} is non empty Element of bool (PARTITIONS Y)
{A,B} is non empty set
{A,B} \/ {C} is non empty set
rng (((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) is set
{((((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . A),((((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . B),((((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . C)} is non empty set
z is set
u is set
(((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . u is set
z is set
u is set
(((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A)))) . u is set
z is Element of bool (bool Y)
Intersect z is Element of bool Y
u is set
meet (rng (((B .--> (EqClass (E,B))) +* (C .--> (EqClass (E,C)))) +* (A .--> (EqClass (D,A))))) is set
h is set
L is Element of Y
EqClass (L,C) is Element of C
(EqClass (D,A)) /\ (EqClass (L,C)) is Element of bool Y
INTERSECTION (A,C) is set
(INTERSECTION (A,C)) \ {{}} is Element of bool (INTERSECTION (A,C))
bool (INTERSECTION (A,C)) is non empty set
A '/\' C is non empty with_non-empty_elements a_partition of Y
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
{A,B,B,D} is non empty set
{E} is non empty Element of bool (PARTITIONS Y)
{A,B,B,D} \/ {E} is non empty set
{B,B,A,D} is non empty set
{B,B,A,D} \/ {E} is non empty set
{B,B,A,D,E} is non empty set
{B,A,D,E} is non empty set
{A,B,D,E} is non empty set
B '/\' D is non empty with_non-empty_elements a_partition of Y
(B '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
{A,B,C,B} is non empty set
{E} is non empty Element of bool (PARTITIONS Y)
{A,B,C,B} \/ {E} is non empty set
{B,B,A,C} is non empty set
{B,B,A,C} \/ {E} is non empty set
{B,B,A,C,E} is non empty set
{B,A,C,E} is non empty set
{A,B,C,E} is non empty set
(B '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
B '/\' D is non empty with_non-empty_elements a_partition of Y
(B '/\' D) '/\' C is non empty with_non-empty_elements a_partition of Y
((B '/\' D) '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
{B,C,D,B} is non empty set
{A} \/ {B,C,D,B} is non empty set
{B,B,C,D} is non empty set
{A} \/ {B,B,C,D} is non empty set
{B,C,D} is non empty set
{A} \/ {B,C,D} is non empty set
{A,B,C,D} is non empty set
B '/\' E is non empty with_non-empty_elements a_partition of Y
(B '/\' E) '/\' C is non empty with_non-empty_elements a_partition of Y
((B '/\' E) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
C '/\' D is non empty with_non-empty_elements a_partition of Y
(B '/\' E) '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
{A,B,C,C} is non empty set
{E} is non empty Element of bool (PARTITIONS Y)
{A,B,C,C} \/ {E} is non empty set
{C,C,A,B} is non empty set
{C,C,A,B} \/ {E} is non empty set
{C,A,B} is non empty set
{C,A,B} \/ {E} is non empty set
{C,A,B,E} is non empty set
{A,B,C,E} is non empty set
(B '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
C '/\' D is non empty with_non-empty_elements a_partition of Y
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
{B,C,D,C} is non empty set
{A} \/ {B,C,D,C} is non empty set
{C,C,B,D} is non empty set
{A} \/ {C,C,B,D} is non empty set
{C,B,D} is non empty set
{A} \/ {C,B,D} is non empty set
{A,C,B,D} is non empty set
{A,B,C,D} is non empty set
C '/\' E is non empty with_non-empty_elements a_partition of Y
B '/\' (C '/\' E) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' E)) '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' E) '/\' D is non empty with_non-empty_elements a_partition of Y
B '/\' ((C '/\' E) '/\' D) is non empty with_non-empty_elements a_partition of Y
C '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
B '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
{B,C,D,D} is non empty set
{A} \/ {B,C,D,D} is non empty set
{D,D,B,C} is non empty set
{A} \/ {D,D,B,C} is non empty set
{D,B,C} is non empty set
{A} \/ {D,B,C} is non empty set
{A,D,B,C} is non empty set
{A,B,C,D} is non empty set
D '/\' E is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' (D '/\' E) is non empty with_non-empty_elements a_partition of Y
C '/\' (D '/\' E) is non empty with_non-empty_elements a_partition of Y
B '/\' (C '/\' (D '/\' E)) is non empty with_non-empty_elements a_partition of Y
C '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
B '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
G \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E} is non empty set
{A} \/ {B,C,D,E} is non empty set
({A} \/ {B,C,D,E}) \ {A} is Element of bool ({A} \/ {B,C,D,E})
bool ({A} \/ {B,C,D,E}) is non empty set
{A} \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E} \ {A} is Element of bool {B,C,D,E}
bool {B,C,D,E} is non empty set
({A} \ {A}) \/ ({B,C,D,E} \ {A}) is set
{B} is non empty Element of bool (PARTITIONS Y)
{C,D,E} is non empty set
{B} \/ {C,D,E} is non empty set
({B} \/ {C,D,E}) \ {A} is Element of bool ({B} \/ {C,D,E})
bool ({B} \/ {C,D,E}) is non empty set
{B} \ {A} is Element of bool (PARTITIONS Y)
{C,D,E} \ {A} is Element of bool {C,D,E}
bool {C,D,E} is non empty set
({B} \ {A}) \/ ({C,D,E} \ {A}) is set
{B} \/ ({C,D,E} \ {A}) is non empty set
{C} is non empty Element of bool (PARTITIONS Y)
{D,E} is non empty set
{C} \/ {D,E} is non empty set
({C} \/ {D,E}) \ {A} is Element of bool ({C} \/ {D,E})
bool ({C} \/ {D,E}) is non empty set
{B} \/ (({C} \/ {D,E}) \ {A}) is non empty set
{C} \ {A} is Element of bool (PARTITIONS Y)
{D,E} \ {A} is Element of bool {D,E}
bool {D,E} is non empty set
({C} \ {A}) \/ ({D,E} \ {A}) is set
{B} \/ (({C} \ {A}) \/ ({D,E} \ {A})) is non empty set
({C} \ {A}) \/ {D,E} is non empty set
{B} \/ (({C} \ {A}) \/ {D,E}) is non empty set
{B} \/ ({C} \/ {D,E}) is non empty set
({A} \ {A}) \/ {B,C,D,E} is non empty set
'/\' (G \ {A}) is non empty with_non-empty_elements a_partition of Y
F is set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
J is set
M is set
J /\ M is set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
N is set
z is set
N /\ z is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
u is set
h is set
u /\ h is set
B .--> u is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> u is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{u}) Element of bool [:{B},{u}:]
{u} is non empty set
[:{B},{u}:] is non empty set
bool [:{B},{u}:] is non empty set
C .--> h is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> h is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{h}) Element of bool [:{C},{h}:]
{h} is non empty set
[:{C},{h}:] is non empty set
bool [:{C},{h}:] is non empty set
(B .--> u) +* (C .--> h) is Relation-like bool (bool Y) -defined Function-like set
D .--> z is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> z is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{z}) Element of bool [:{D},{z}:]
{z} is non empty set
[:{D},{z}:] is non empty set
bool [:{D},{z}:] is non empty set
((B .--> u) +* (C .--> h)) +* (D .--> z) is Relation-like bool (bool Y) -defined Function-like set
E .--> M is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> M is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{M}) Element of bool [:{E},{M}:]
{M} is non empty set
[:{E},{M}:] is non empty set
bool [:{E},{M}:] is non empty set
(((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M) is Relation-like bool (bool Y) -defined Function-like set
dom (C .--> h) is set
dom (D .--> z) is set
{D} is non empty Element of bool (PARTITIONS Y)
dom (E .--> M) is set
{E} is non empty Element of bool (PARTITIONS Y)
((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . E is set
(E .--> M) . E is set
((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . C is set
(((B .--> u) +* (C .--> h)) +* (D .--> z)) . C is set
((B .--> u) +* (C .--> h)) . C is set
(C .--> h) . C is set
((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . D is set
(((B .--> u) +* (C .--> h)) +* (D .--> z)) . D is set
(D .--> z) . D is set
((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . B is set
(((B .--> u) +* (C .--> h)) +* (D .--> z)) . B is set
((B .--> u) +* (C .--> h)) . B is set
(B .--> u) . B is set
GG is set
((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . GG is set
dom ((B .--> u) +* (C .--> h)) is set
dom (B .--> u) is set
(dom (B .--> u)) \/ (dom (C .--> h)) is set
dom (((B .--> u) +* (C .--> h)) +* (D .--> z)) is set
((dom (B .--> u)) \/ (dom (C .--> h))) \/ (dom (D .--> z)) is set
dom ((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) is set
(((dom (B .--> u)) \/ (dom (C .--> h))) \/ (dom (D .--> z))) \/ (dom (E .--> M)) is set
{B} \/ {C} is non empty Element of bool (PARTITIONS Y)
({B} \/ {C}) \/ {D} is non empty Element of bool (PARTITIONS Y)
(({B} \/ {C}) \/ {D}) \/ {E} is non empty Element of bool (PARTITIONS Y)
{B,C} is non empty set
{B,C} \/ {D} is non empty set
({B,C} \/ {D}) \/ {E} is non empty set
{B,C,D} is non empty set
{B,C,D} \/ {E} is non empty set
rng ((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) is set
{(((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . D),(((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . B),(((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . C),(((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . E)} is non empty set
GG is set
I is set
((((B .--> u) +* (C .--> h)) +* (D .--> z)) +* (E .--> M)) . I is set
GG is set
I is set
GG is Element of bool (bool Y)
Intersect GG is Element of bool Y
HH is set
I is Relation-like Function-like set
I . D is set
I . B is set
I . C is set
I . E is set
{(I . D),(I . B),(I . C),(I . E)} is non empty set
FF is set
(u /\ h) /\ M is set
z /\ ((u /\ h) /\ M) is set
z /\ u is set
h /\ (z /\ u) is set
(h /\ (z /\ u)) /\ M is set
(z /\ u) /\ M is set
h /\ ((z /\ u) /\ M) is set
z /\ M is set
(z /\ M) /\ u is set
h /\ ((z /\ M) /\ u) is set
h /\ (z /\ M) is set
(h /\ (z /\ M)) /\ u is set
u /\ z is set
h /\ (u /\ z) is set
(h /\ (u /\ z)) /\ M is set
(u /\ z) /\ M is set
h /\ ((u /\ z) /\ M) is set
meet GG is Element of bool Y
I is Relation-like Function-like set
rng I is set
HH is set
meet (rng I) is set
I . D is set
I . C is set
I . B is set
(u /\ h) /\ z is set
I . E is set
F is set
J is Relation-like Function-like set
dom J is set
rng J is set
M is Element of bool (bool Y)
Intersect M is Element of bool Y
J . D is set
J . B is set
J . C is set
(J . B) /\ (J . C) is set
J . E is set
((J . B) /\ (J . C)) /\ (J . D) is set
(((J . B) /\ (J . C)) /\ (J . D)) /\ (J . E) is set
u is set
meet (rng J) is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
u is set
{(J . B),(J . C),(J . D),(J . E)} is non empty set
h is set
L is set
J . L is set
h is set
meet (rng J) is set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E} is non empty set
{A,B} \/ {C,D,E} is non empty set
{B,A,C,D,E} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
CompF (C,G) is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
((A '/\' B) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E} is non empty set
{A,B,C} \/ {D,E} is non empty set
{A} is non empty Element of bool (PARTITIONS Y)
{B,C} is non empty set
{A} \/ {B,C} is non empty set
({A} \/ {B,C}) \/ {D,E} is non empty set
{A,C,B} is non empty set
{A,C,B} \/ {D,E} is non empty set
{A,C} is non empty set
{B} is non empty Element of bool (PARTITIONS Y)
{A,C} \/ {B} is non empty set
({A,C} \/ {B}) \/ {D,E} is non empty set
{C,A,B} is non empty set
{C,A,B} \/ {D,E} is non empty set
{C,A,B,D,E} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
CompF (D,G) is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
((A '/\' B) '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E} is non empty set
{A,B} \/ {C,D,E} is non empty set
{C,D} is non empty set
{E} is non empty Element of bool (PARTITIONS Y)
{C,D} \/ {E} is non empty set
{A,B} \/ ({C,D} \/ {E}) is non empty set
{D,C,E} is non empty set
{A,B} \/ {D,C,E} is non empty set
{A,B,D,C,E} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
CompF (E,G) is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E} is non empty set
{A,B,C} \/ {D,E} is non empty set
{A,B,C,E,D} is non empty set
Y is set
G is set
A is set
B is set
C is set
D is Relation-like Function-like set
D . Y is set
D . G is set
D . A is set
D . B is set
D . C is set
F is set
G .--> F is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> F is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{F}) Element of bool [:{G},{F}:]
{F} is non empty set
[:{G},{F}:] is non empty set
bool [:{G},{F}:] is non empty set
J is set
A .--> J is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> J is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{J}) Element of bool [:{A},{J}:]
{J} is non empty set
[:{A},{J}:] is non empty set
bool [:{A},{J}:] is non empty set
(G .--> F) +* (A .--> J) is Relation-like Function-like set
M is set
B .--> M is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> M is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{M}) Element of bool [:{B},{M}:]
{M} is non empty set
[:{B},{M}:] is non empty set
bool [:{B},{M}:] is non empty set
((G .--> F) +* (A .--> J)) +* (B .--> M) is Relation-like Function-like set
N is set
C .--> N is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> N is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{N}) Element of bool [:{C},{N}:]
{N} is non empty set
[:{C},{N}:] is non empty set
bool [:{C},{N}:] is non empty set
(((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N) is Relation-like Function-like set
E is set
Y .--> E is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> E is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{E}) Element of bool [:{Y},{E}:]
{E} is non empty set
[:{Y},{E}:] is non empty set
bool [:{Y},{E}:] is non empty set
((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) +* (Y .--> E) is Relation-like Function-like set
dom (Y .--> E) is set
(Y .--> E) . Y is set
((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) . A is set
dom (B .--> M) is set
(((G .--> F) +* (A .--> J)) +* (B .--> M)) . G is set
((G .--> F) +* (A .--> J)) . G is set
((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) . C is set
dom (C .--> N) is set
(C .--> N) . C is set
(((G .--> F) +* (A .--> J)) +* (B .--> M)) . A is set
((G .--> F) +* (A .--> J)) . A is set
dom (A .--> J) is set
(A .--> J) . A is set
((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) . B is set
(((G .--> F) +* (A .--> J)) +* (B .--> M)) . B is set
(B .--> M) . B is set
((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) . G is set
(G .--> F) . G is set
G is set
A is set
B is set
C is set
Y is set
{Y,G,A,B,C} is non empty set
D is Relation-like Function-like set
dom D is set
F is set
G .--> F is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> F is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{F}) Element of bool [:{G},{F}:]
{F} is non empty set
[:{G},{F}:] is non empty set
bool [:{G},{F}:] is non empty set
J is set
A .--> J is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> J is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{J}) Element of bool [:{A},{J}:]
{J} is non empty set
[:{A},{J}:] is non empty set
bool [:{A},{J}:] is non empty set
(G .--> F) +* (A .--> J) is Relation-like Function-like set
M is set
B .--> M is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> M is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{M}) Element of bool [:{B},{M}:]
{M} is non empty set
[:{B},{M}:] is non empty set
bool [:{B},{M}:] is non empty set
((G .--> F) +* (A .--> J)) +* (B .--> M) is Relation-like Function-like set
N is set
C .--> N is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> N is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{N}) Element of bool [:{C},{N}:]
{N} is non empty set
[:{C},{N}:] is non empty set
bool [:{C},{N}:] is non empty set
(((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N) is Relation-like Function-like set
E is set
Y .--> E is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> E is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{E}) Element of bool [:{Y},{E}:]
{E} is non empty set
[:{Y},{E}:] is non empty set
bool [:{Y},{E}:] is non empty set
((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) +* (Y .--> E) is Relation-like Function-like set
dom (B .--> M) is set
dom (C .--> N) is set
dom ((G .--> F) +* (A .--> J)) is set
dom (G .--> F) is set
dom (A .--> J) is set
(dom (G .--> F)) \/ (dom (A .--> J)) is set
dom (((G .--> F) +* (A .--> J)) +* (B .--> M)) is set
((dom (G .--> F)) \/ (dom (A .--> J))) \/ (dom (B .--> M)) is set
dom ((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) is set
(((dom (G .--> F)) \/ (dom (A .--> J))) \/ (dom (B .--> M))) \/ (dom (C .--> N)) is set
dom (((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) +* (Y .--> E)) is set
dom (Y .--> E) is set
((((dom (G .--> F)) \/ (dom (A .--> J))) \/ (dom (B .--> M))) \/ (dom (C .--> N))) \/ (dom (Y .--> E)) is set
{G} \/ {A} is non empty set
({G} \/ {A}) \/ {B} is non empty set
(({G} \/ {A}) \/ {B}) \/ {C} is non empty set
{Y} \/ ((({G} \/ {A}) \/ {B}) \/ {C}) is non empty set
{G,A} is non empty set
{G,A} \/ {B} is non empty set
({G,A} \/ {B}) \/ {C} is non empty set
{Y} \/ (({G,A} \/ {B}) \/ {C}) is non empty set
{G,A,B} is non empty set
{G,A,B} \/ {C} is non empty set
{Y} \/ ({G,A,B} \/ {C}) is non empty set
{G,A,B,C} is non empty set
{Y} \/ {G,A,B,C} is non empty set
G is set
A is set
B is set
C is set
Y is set
D is Relation-like Function-like set
rng D is set
D . Y is set
D . G is set
D . A is set
D . B is set
D . C is set
{(D . Y),(D . G),(D . A),(D . B),(D . C)} is non empty set
F is set
G .--> F is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> F is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{F}) Element of bool [:{G},{F}:]
{F} is non empty set
[:{G},{F}:] is non empty set
bool [:{G},{F}:] is non empty set
J is set
A .--> J is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> J is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{J}) Element of bool [:{A},{J}:]
{J} is non empty set
[:{A},{J}:] is non empty set
bool [:{A},{J}:] is non empty set
(G .--> F) +* (A .--> J) is Relation-like Function-like set
M is set
B .--> M is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> M is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{M}) Element of bool [:{B},{M}:]
{M} is non empty set
[:{B},{M}:] is non empty set
bool [:{B},{M}:] is non empty set
((G .--> F) +* (A .--> J)) +* (B .--> M) is Relation-like Function-like set
N is set
C .--> N is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> N is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{N}) Element of bool [:{C},{N}:]
{N} is non empty set
[:{C},{N}:] is non empty set
bool [:{C},{N}:] is non empty set
(((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N) is Relation-like Function-like set
E is set
Y .--> E is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> E is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{E}) Element of bool [:{Y},{E}:]
{E} is non empty set
[:{Y},{E}:] is non empty set
bool [:{Y},{E}:] is non empty set
((((G .--> F) +* (A .--> J)) +* (B .--> M)) +* (C .--> N)) +* (Y .--> E) is Relation-like Function-like set
dom D is set
{Y,G,A,B,C} is non empty set
z is set
u is set
D . u is set
z is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
J is Element of Y
EqClass (J,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
F is Element of Y
EqClass (F,A) is Element of A
EqClass (J,B) is Element of B
B .--> (EqClass (J,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (J,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (J,B))}) Element of bool [:{B},{(EqClass (J,B))}:]
{(EqClass (J,B))} is non empty set
[:{B},{(EqClass (J,B))}:] is non empty set
bool [:{B},{(EqClass (J,B))}:] is non empty set
EqClass (J,C) is Element of C
C .--> (EqClass (J,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (J,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (J,C))}) Element of bool [:{C},{(EqClass (J,C))}:]
{(EqClass (J,C))} is non empty set
[:{C},{(EqClass (J,C))}:] is non empty set
bool [:{C},{(EqClass (J,C))}:] is non empty set
(B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (J,D) is Element of D
D .--> (EqClass (J,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (J,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (J,D))}) Element of bool [:{D},{(EqClass (J,D))}:]
{(EqClass (J,D))} is non empty set
[:{D},{(EqClass (J,D))}:] is non empty set
bool [:{D},{(EqClass (J,D))}:] is non empty set
((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (J,E) is Element of E
E .--> (EqClass (J,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (J,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (J,E))}) Element of bool [:{E},{(EqClass (J,E))}:]
{(EqClass (J,E))} is non empty set
[:{E},{(EqClass (J,E))}:] is non empty set
bool [:{E},{(EqClass (J,E))}:] is non empty set
(((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E))) is Relation-like bool (bool Y) -defined Function-like set
A .--> (EqClass (F,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (F,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (F,A))}) Element of bool [:{A},{(EqClass (F,A))}:]
{(EqClass (F,A))} is non empty set
[:{A},{(EqClass (F,A))}:] is non empty set
bool [:{A},{(EqClass (F,A))}:] is non empty set
((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A))) is Relation-like bool (bool Y) -defined Function-like set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . B is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . D is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . C is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . E is set
rng (((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . A is set
{((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . A),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . B),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . C),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . D),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . E)} is non empty set
z is set
dom (((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) is set
u is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . u is set
z is Element of bool (bool Y)
Intersect z is Element of bool Y
u is set
meet z is Element of bool Y
(EqClass (J,B)) /\ (EqClass (J,C)) is Element of bool Y
((EqClass (J,B)) /\ (EqClass (J,C))) /\ (EqClass (J,D)) is Element of bool Y
(((EqClass (J,B)) /\ (EqClass (J,C))) /\ (EqClass (J,D))) /\ (EqClass (J,E)) is Element of bool Y
EqClass (J,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (J,((B '/\' C) '/\' D))) /\ (EqClass (J,E)) is Element of bool Y
EqClass (J,(B '/\' C)) is Element of B '/\' C
(EqClass (J,(B '/\' C))) /\ (EqClass (J,D)) is Element of bool Y
((EqClass (J,(B '/\' C))) /\ (EqClass (J,D))) /\ (EqClass (J,E)) is Element of bool Y
((((EqClass (J,B)) /\ (EqClass (J,C))) /\ (EqClass (J,D))) /\ (EqClass (J,E))) /\ (EqClass (F,A)) is Element of bool Y
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
C '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
F is Element of Y
EqClass (F,((C '/\' D) '/\' E)) is Element of (C '/\' D) '/\' E
J is Element of Y
EqClass (J,((C '/\' D) '/\' E)) is Element of (C '/\' D) '/\' E
EqClass (J,(CompF (A,G))) is Element of CompF (A,G)
EqClass (F,(CompF (B,G))) is Element of CompF (B,G)
EqClass (J,B) is Element of B
B .--> (EqClass (J,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (J,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (J,B))}) Element of bool [:{B},{(EqClass (J,B))}:]
{(EqClass (J,B))} is non empty set
[:{B},{(EqClass (J,B))}:] is non empty set
bool [:{B},{(EqClass (J,B))}:] is non empty set
EqClass (J,C) is Element of C
C .--> (EqClass (J,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (J,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (J,C))}) Element of bool [:{C},{(EqClass (J,C))}:]
{(EqClass (J,C))} is non empty set
[:{C},{(EqClass (J,C))}:] is non empty set
bool [:{C},{(EqClass (J,C))}:] is non empty set
(B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (J,D) is Element of D
D .--> (EqClass (J,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (J,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (J,D))}) Element of bool [:{D},{(EqClass (J,D))}:]
{(EqClass (J,D))} is non empty set
[:{D},{(EqClass (J,D))}:] is non empty set
bool [:{D},{(EqClass (J,D))}:] is non empty set
((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (J,E) is Element of E
E .--> (EqClass (J,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (J,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (J,E))}) Element of bool [:{E},{(EqClass (J,E))}:]
{(EqClass (J,E))} is non empty set
[:{E},{(EqClass (J,E))}:] is non empty set
bool [:{E},{(EqClass (J,E))}:] is non empty set
(((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (F,A) is Element of A
A .--> (EqClass (F,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (F,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (F,A))}) Element of bool [:{A},{(EqClass (F,A))}:]
{(EqClass (F,A))} is non empty set
[:{A},{(EqClass (F,A))}:] is non empty set
bool [:{A},{(EqClass (F,A))}:] is non empty set
((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A))) is Relation-like bool (bool Y) -defined Function-like set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . B is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . E is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . D is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . C is set
rng (((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . A is set
{((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . A),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . B),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . C),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . D),((((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . E)} is non empty set
N is set
dom (((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) is set
z is set
(((((B .--> (EqClass (J,B))) +* (C .--> (EqClass (J,C)))) +* (D .--> (EqClass (J,D)))) +* (E .--> (EqClass (J,E)))) +* (A .--> (EqClass (F,A)))) . z is set
N is Element of bool (bool Y)
Intersect N is Element of bool Y
z is set
meet N is Element of bool Y
(EqClass (J,B)) /\ (EqClass (J,C)) is Element of bool Y
((EqClass (J,B)) /\ (EqClass (J,C))) /\ (EqClass (J,D)) is Element of bool Y
(((EqClass (J,B)) /\ (EqClass (J,C))) /\ (EqClass (J,D))) /\ (EqClass (J,E)) is Element of bool Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
EqClass (J,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
EqClass (J,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (J,((B '/\' C) '/\' D))) /\ (EqClass (J,E)) is Element of bool Y
EqClass (J,(B '/\' C)) is Element of B '/\' C
(EqClass (J,(B '/\' C))) /\ (EqClass (J,D)) is Element of bool Y
((EqClass (J,(B '/\' C))) /\ (EqClass (J,D))) /\ (EqClass (J,E)) is Element of bool Y
((((EqClass (J,B)) /\ (EqClass (J,C))) /\ (EqClass (J,D))) /\ (EqClass (J,E))) /\ (EqClass (F,A)) is Element of bool Y
(EqClass (J,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (F,A)) is Element of bool Y
L is set
GG is Element of Y
EqClass (GG,((C '/\' D) '/\' E)) is Element of (C '/\' D) '/\' E
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
EqClass (J,((B '/\' (C '/\' D)) '/\' E)) is Element of (B '/\' (C '/\' D)) '/\' E
B '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
EqClass (J,(B '/\' ((C '/\' D) '/\' E))) is Element of B '/\' ((C '/\' D) '/\' E)
(EqClass (F,A)) /\ (EqClass (GG,((C '/\' D) '/\' E))) is Element of bool Y
A '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
A '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(A '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
INTERSECTION (A,((C '/\' D) '/\' E)) is set
(INTERSECTION (A,((C '/\' D) '/\' E))) \ {{}} is Element of bool (INTERSECTION (A,((C '/\' D) '/\' E)))
bool (INTERSECTION (A,((C '/\' D) '/\' E))) is non empty set
(EqClass (J,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (F,(CompF (B,G)))) is Element of bool Y
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
G \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E,F} is non empty set
{A} \/ {B,C,D,E,F} is non empty set
({A} \/ {B,C,D,E,F}) \ {A} is Element of bool ({A} \/ {B,C,D,E,F})
bool ({A} \/ {B,C,D,E,F}) is non empty set
{A} \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E,F} \ {A} is Element of bool {B,C,D,E,F}
bool {B,C,D,E,F} is non empty set
({A} \ {A}) \/ ({B,C,D,E,F} \ {A}) is set
{B} is non empty Element of bool (PARTITIONS Y)
{C,D,E,F} is non empty set
{B} \/ {C,D,E,F} is non empty set
({B} \/ {C,D,E,F}) \ {A} is Element of bool ({B} \/ {C,D,E,F})
bool ({B} \/ {C,D,E,F}) is non empty set
{B} \ {A} is Element of bool (PARTITIONS Y)
{C,D,E,F} \ {A} is Element of bool {C,D,E,F}
bool {C,D,E,F} is non empty set
({B} \ {A}) \/ ({C,D,E,F} \ {A}) is set
{B} \/ ({C,D,E,F} \ {A}) is non empty set
{C} is non empty Element of bool (PARTITIONS Y)
{D,E,F} is non empty set
{C} \/ {D,E,F} is non empty set
({C} \/ {D,E,F}) \ {A} is Element of bool ({C} \/ {D,E,F})
bool ({C} \/ {D,E,F}) is non empty set
{B} \/ (({C} \/ {D,E,F}) \ {A}) is non empty set
{C} \ {A} is Element of bool (PARTITIONS Y)
{D,E,F} \ {A} is Element of bool {D,E,F}
bool {D,E,F} is non empty set
({C} \ {A}) \/ ({D,E,F} \ {A}) is set
{B} \/ (({C} \ {A}) \/ ({D,E,F} \ {A})) is non empty set
{D,E} is non empty set
{F} is non empty Element of bool (PARTITIONS Y)
{D,E} \/ {F} is non empty set
({D,E} \/ {F}) \ {A} is Element of bool ({D,E} \/ {F})
bool ({D,E} \/ {F}) is non empty set
({C} \ {A}) \/ (({D,E} \/ {F}) \ {A}) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \/ {F}) \ {A})) is non empty set
{D,E} \ {A} is Element of bool {D,E}
bool {D,E} is non empty set
{F} \ {A} is Element of bool (PARTITIONS Y)
({D,E} \ {A}) \/ ({F} \ {A}) is set
({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F} \ {A})) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F} \ {A}))) is non empty set
{D,E} \/ ({F} \ {A}) is non empty set
({C} \ {A}) \/ ({D,E} \/ ({F} \ {A})) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ ({F} \ {A}))) is non empty set
({C} \ {A}) \/ ({D,E} \/ {F}) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ {F})) is non empty set
{C} \/ ({D,E} \/ {F}) is non empty set
{B} \/ ({C} \/ ({D,E} \/ {F})) is non empty set
{B} \/ ({C} \/ {D,E,F}) is non empty set
'/\' (G \ {A}) is non empty with_non-empty_elements a_partition of Y
J is set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
M is set
N is set
M /\ N is set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
z is set
u is set
z /\ u is set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
h is set
L is set
h /\ L is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
GG is set
I is set
GG /\ I is set
B .--> GG is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> GG is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{GG}) Element of bool [:{B},{GG}:]
{GG} is non empty set
[:{B},{GG}:] is non empty set
bool [:{B},{GG}:] is non empty set
C .--> I is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> I is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{I}) Element of bool [:{C},{I}:]
{I} is non empty set
[:{C},{I}:] is non empty set
bool [:{C},{I}:] is non empty set
(B .--> GG) +* (C .--> I) is Relation-like bool (bool Y) -defined Function-like set
D .--> L is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> L is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{L}) Element of bool [:{D},{L}:]
{L} is non empty set
[:{D},{L}:] is non empty set
bool [:{D},{L}:] is non empty set
((B .--> GG) +* (C .--> I)) +* (D .--> L) is Relation-like bool (bool Y) -defined Function-like set
E .--> u is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> u is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{u}) Element of bool [:{E},{u}:]
{u} is non empty set
[:{E},{u}:] is non empty set
bool [:{E},{u}:] is non empty set
(((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u) is Relation-like bool (bool Y) -defined Function-like set
F .--> N is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> N is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{N}) Element of bool [:{F},{N}:]
{N} is non empty set
[:{F},{N}:] is non empty set
bool [:{F},{N}:] is non empty set
((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N) is Relation-like bool (bool Y) -defined Function-like set
(((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . B is set
(((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . E is set
(((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . F is set
dom (((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) is set
{F,B,C,D,E} is non empty set
{B,C,D,E} is non empty set
{F} \/ {B,C,D,E} is non empty set
(((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . C is set
rng (((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) is set
(((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . D is set
{((((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . D),((((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . B),((((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . C),((((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . E),((((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . F)} is non empty set
FF is set
m is set
(((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . m is set
FF is set
FF is Element of bool (bool Y)
Intersect FF is Element of bool Y
meet (rng (((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N))) is set
m is set
m is set
p is set
(GG /\ I) /\ u is set
L /\ ((GG /\ I) /\ u) is set
(L /\ ((GG /\ I) /\ u)) /\ N is set
((GG /\ I) /\ u) /\ N is set
L /\ (((GG /\ I) /\ u) /\ N) is set
L /\ GG is set
I /\ (L /\ GG) is set
(I /\ (L /\ GG)) /\ u is set
((I /\ (L /\ GG)) /\ u) /\ N is set
(L /\ GG) /\ u is set
I /\ ((L /\ GG) /\ u) is set
(I /\ ((L /\ GG) /\ u)) /\ N is set
L /\ u is set
(L /\ u) /\ GG is set
I /\ ((L /\ u) /\ GG) is set
(I /\ ((L /\ u) /\ GG)) /\ N is set
((L /\ u) /\ GG) /\ N is set
I /\ (((L /\ u) /\ GG) /\ N) is set
N /\ GG is set
(L /\ u) /\ (N /\ GG) is set
I /\ ((L /\ u) /\ (N /\ GG)) is set
I /\ (L /\ u) is set
(I /\ (L /\ u)) /\ (N /\ GG) is set
(I /\ (L /\ u)) /\ N is set
((I /\ (L /\ u)) /\ N) /\ GG is set
GG /\ L is set
I /\ (GG /\ L) is set
(I /\ (GG /\ L)) /\ u is set
((I /\ (GG /\ L)) /\ u) /\ N is set
(GG /\ L) /\ u is set
I /\ ((GG /\ L) /\ u) is set
(I /\ ((GG /\ L) /\ u)) /\ N is set
((GG /\ L) /\ u) /\ N is set
I /\ (((GG /\ L) /\ u) /\ N) is set
(GG /\ I) /\ L is set
((GG /\ I) /\ L) /\ N is set
(((GG /\ I) /\ L) /\ N) /\ u is set
meet FF is Element of bool Y
m is set
(((((B .--> GG) +* (C .--> I)) +* (D .--> L)) +* (E .--> u)) +* (F .--> N)) . m is set
m is set
(GG /\ I) /\ L is set
((GG /\ I) /\ L) /\ u is set
J is set
M is Relation-like Function-like set
dom M is set
rng M is set
N is Element of bool (bool Y)
Intersect N is Element of bool Y
M . C is set
M . B is set
(M . B) /\ (M . C) is set
INTERSECTION (B,C) is set
M . D is set
((M . B) /\ (M . C)) /\ (M . D) is set
M . E is set
meet (rng M) is set
M . F is set
(((M . B) /\ (M . C)) /\ (M . D)) /\ (M . E) is set
((((M . B) /\ (M . C)) /\ (M . D)) /\ (M . E)) /\ (M . F) is set
h is set
h is set
{(M . B),(M . C),(M . D),(M . E),(M . F)} is non empty set
L is set
GG is set
M . GG is set
L is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
{B,A} is non empty set
{C,D,E,F} is non empty set
{B,A} \/ {C,D,E,F} is non empty set
{B,A,C,D,E,F} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
CompF (C,G) is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
(((A '/\' B) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F} is non empty set
{A,B,C} \/ {D,E,F} is non empty set
{A} is non empty Element of bool (PARTITIONS Y)
{B,C} is non empty set
{A} \/ {B,C} is non empty set
({A} \/ {B,C}) \/ {D,E,F} is non empty set
{A,C,B} is non empty set
{A,C,B} \/ {D,E,F} is non empty set
{A,C,B,D,E,F} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
CompF (D,G) is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
(((A '/\' B) '/\' C) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E,F} is non empty set
{A,B} \/ {C,D,E,F} is non empty set
{C,D} is non empty set
{E,F} is non empty set
{C,D} \/ {E,F} is non empty set
{A,B} \/ ({C,D} \/ {E,F}) is non empty set
{D,C,E,F} is non empty set
{A,B} \/ {D,C,E,F} is non empty set
{A,B,D,C,E,F} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
CompF (E,G) is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
(((A '/\' B) '/\' C) '/\' D) '/\' F is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F} is non empty set
{A,B,C} \/ {D,E,F} is non empty set
{D,E} is non empty set
{F} is non empty Element of bool (PARTITIONS Y)
{D,E} \/ {F} is non empty set
{A,B,C} \/ ({D,E} \/ {F}) is non empty set
{E,D,F} is non empty set
{A,B,C} \/ {E,D,F} is non empty set
{A,B,C,E,D,F} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
CompF (F,G) is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
{E,F} is non empty set
{A,B,C,D} \/ {E,F} is non empty set
{A,B,C,D,F,E} is non empty set
Y is set
G is set
A is set
B is set
C is set
D is set
E is Relation-like Function-like set
E . Y is set
E . G is set
E . A is set
E . B is set
E . C is set
E . D is set
J is set
G .--> J is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> J is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{J}) Element of bool [:{G},{J}:]
{J} is non empty set
[:{G},{J}:] is non empty set
bool [:{G},{J}:] is non empty set
M is set
A .--> M is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> M is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{M}) Element of bool [:{A},{M}:]
{M} is non empty set
[:{A},{M}:] is non empty set
bool [:{A},{M}:] is non empty set
(G .--> J) +* (A .--> M) is Relation-like Function-like set
N is set
B .--> N is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> N is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{N}) Element of bool [:{B},{N}:]
{N} is non empty set
[:{B},{N}:] is non empty set
bool [:{B},{N}:] is non empty set
((G .--> J) +* (A .--> M)) +* (B .--> N) is Relation-like Function-like set
z is set
C .--> z is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> z is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{z}) Element of bool [:{C},{z}:]
{z} is non empty set
[:{C},{z}:] is non empty set
bool [:{C},{z}:] is non empty set
(((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z) is Relation-like Function-like set
u is set
D .--> u is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> u is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{u}) Element of bool [:{D},{u}:]
{u} is non empty set
[:{D},{u}:] is non empty set
bool [:{D},{u}:] is non empty set
((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u) is Relation-like Function-like set
F is set
Y .--> F is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> F is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{F}) Element of bool [:{Y},{F}:]
{F} is non empty set
[:{Y},{F}:] is non empty set
bool [:{Y},{F}:] is non empty set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) +* (Y .--> F) is Relation-like Function-like set
dom (Y .--> F) is set
(Y .--> F) . Y is set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) . A is set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) . D is set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) . C is set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) . B is set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) . G is set
G is set
A is set
B is set
C is set
D is set
Y is set
{Y,G,A,B,C,D} is non empty set
E is Relation-like Function-like set
dom E is set
J is set
G .--> J is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> J is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{J}) Element of bool [:{G},{J}:]
{J} is non empty set
[:{G},{J}:] is non empty set
bool [:{G},{J}:] is non empty set
M is set
A .--> M is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> M is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{M}) Element of bool [:{A},{M}:]
{M} is non empty set
[:{A},{M}:] is non empty set
bool [:{A},{M}:] is non empty set
(G .--> J) +* (A .--> M) is Relation-like Function-like set
N is set
B .--> N is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> N is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{N}) Element of bool [:{B},{N}:]
{N} is non empty set
[:{B},{N}:] is non empty set
bool [:{B},{N}:] is non empty set
((G .--> J) +* (A .--> M)) +* (B .--> N) is Relation-like Function-like set
z is set
C .--> z is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> z is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{z}) Element of bool [:{C},{z}:]
{z} is non empty set
[:{C},{z}:] is non empty set
bool [:{C},{z}:] is non empty set
(((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z) is Relation-like Function-like set
u is set
D .--> u is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> u is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{u}) Element of bool [:{D},{u}:]
{u} is non empty set
[:{D},{u}:] is non empty set
bool [:{D},{u}:] is non empty set
((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u) is Relation-like Function-like set
F is set
Y .--> F is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> F is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{F}) Element of bool [:{Y},{F}:]
{F} is non empty set
[:{Y},{F}:] is non empty set
bool [:{Y},{F}:] is non empty set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) +* (Y .--> F) is Relation-like Function-like set
dom (Y .--> F) is set
dom (((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) is set
{D,G,A,B,C} is non empty set
{G,A,B,C} is non empty set
{D} \/ {G,A,B,C} is non empty set
{G,A,B,C,D} is non empty set
dom ((((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) +* (Y .--> F)) is set
{G,A,B,C,D} \/ {Y} is non empty set
G is set
A is set
B is set
C is set
D is set
Y is set
E is Relation-like Function-like set
rng E is set
E . Y is set
E . G is set
E . A is set
E . B is set
E . C is set
E . D is set
{(E . Y),(E . G),(E . A),(E . B),(E . C),(E . D)} is non empty set
J is set
G .--> J is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> J is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{J}) Element of bool [:{G},{J}:]
{J} is non empty set
[:{G},{J}:] is non empty set
bool [:{G},{J}:] is non empty set
M is set
A .--> M is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> M is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{M}) Element of bool [:{A},{M}:]
{M} is non empty set
[:{A},{M}:] is non empty set
bool [:{A},{M}:] is non empty set
(G .--> J) +* (A .--> M) is Relation-like Function-like set
N is set
B .--> N is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> N is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{N}) Element of bool [:{B},{N}:]
{N} is non empty set
[:{B},{N}:] is non empty set
bool [:{B},{N}:] is non empty set
((G .--> J) +* (A .--> M)) +* (B .--> N) is Relation-like Function-like set
z is set
C .--> z is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> z is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{z}) Element of bool [:{C},{z}:]
{z} is non empty set
[:{C},{z}:] is non empty set
bool [:{C},{z}:] is non empty set
(((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z) is Relation-like Function-like set
u is set
D .--> u is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> u is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{u}) Element of bool [:{D},{u}:]
{u} is non empty set
[:{D},{u}:] is non empty set
bool [:{D},{u}:] is non empty set
((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u) is Relation-like Function-like set
F is set
Y .--> F is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> F is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{F}) Element of bool [:{Y},{F}:]
{F} is non empty set
[:{Y},{F}:] is non empty set
bool [:{Y},{F}:] is non empty set
(((((G .--> J) +* (A .--> M)) +* (B .--> N)) +* (C .--> z)) +* (D .--> u)) +* (Y .--> F) is Relation-like Function-like set
dom E is set
{Y,G,A,B,C,D} is non empty set
h is set
L is set
E . L is set
h is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
M is Element of Y
EqClass (M,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
J is Element of Y
EqClass (J,A) is Element of A
EqClass (M,B) is Element of B
B .--> (EqClass (M,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (M,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (M,B))}) Element of bool [:{B},{(EqClass (M,B))}:]
{(EqClass (M,B))} is non empty set
[:{B},{(EqClass (M,B))}:] is non empty set
bool [:{B},{(EqClass (M,B))}:] is non empty set
EqClass (M,C) is Element of C
C .--> (EqClass (M,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (M,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (M,C))}) Element of bool [:{C},{(EqClass (M,C))}:]
{(EqClass (M,C))} is non empty set
[:{C},{(EqClass (M,C))}:] is non empty set
bool [:{C},{(EqClass (M,C))}:] is non empty set
(B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (M,D) is Element of D
D .--> (EqClass (M,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (M,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (M,D))}) Element of bool [:{D},{(EqClass (M,D))}:]
{(EqClass (M,D))} is non empty set
[:{D},{(EqClass (M,D))}:] is non empty set
bool [:{D},{(EqClass (M,D))}:] is non empty set
((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (M,E) is Element of E
E .--> (EqClass (M,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (M,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (M,E))}) Element of bool [:{E},{(EqClass (M,E))}:]
{(EqClass (M,E))} is non empty set
[:{E},{(EqClass (M,E))}:] is non empty set
bool [:{E},{(EqClass (M,E))}:] is non empty set
(((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (M,F) is Element of F
F .--> (EqClass (M,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (M,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (M,F))}) Element of bool [:{F},{(EqClass (M,F))}:]
{(EqClass (M,F))} is non empty set
[:{F},{(EqClass (M,F))}:] is non empty set
bool [:{F},{(EqClass (M,F))}:] is non empty set
((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F))) is Relation-like bool (bool Y) -defined Function-like set
A .--> (EqClass (J,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (J,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (J,A))}) Element of bool [:{A},{(EqClass (J,A))}:]
{(EqClass (J,A))} is non empty set
[:{A},{(EqClass (J,A))}:] is non empty set
bool [:{A},{(EqClass (J,A))}:] is non empty set
(((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A))) is Relation-like bool (bool Y) -defined Function-like set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . A is set
EqClass (M,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (M,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (M,F)) is Element of bool Y
EqClass (M,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (M,((B '/\' C) '/\' D))) /\ (EqClass (M,E)) is Element of bool Y
((EqClass (M,((B '/\' C) '/\' D))) /\ (EqClass (M,E))) /\ (EqClass (M,F)) is Element of bool Y
EqClass (M,(B '/\' C)) is Element of B '/\' C
(EqClass (M,(B '/\' C))) /\ (EqClass (M,D)) is Element of bool Y
((EqClass (M,(B '/\' C))) /\ (EqClass (M,D))) /\ (EqClass (M,E)) is Element of bool Y
(((EqClass (M,(B '/\' C))) /\ (EqClass (M,D))) /\ (EqClass (M,E))) /\ (EqClass (M,F)) is Element of bool Y
(EqClass (M,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (J,A)) is Element of bool Y
(EqClass (M,B)) /\ (EqClass (M,C)) is Element of bool Y
((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D)) is Element of bool Y
(((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D))) /\ (EqClass (M,E)) is Element of bool Y
((((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D))) /\ (EqClass (M,E))) /\ (EqClass (M,F)) is Element of bool Y
(((((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D))) /\ (EqClass (M,E))) /\ (EqClass (M,F))) /\ (EqClass (J,A)) is Element of bool Y
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . B is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . D is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . C is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . F is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . E is set
rng ((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) is set
{(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . A),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . B),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . C),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . D),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . E),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . F)} is non empty set
h is set
dom ((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) is set
h is Element of bool (bool Y)
Intersect h is Element of bool Y
meet (rng ((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A))))) is set
L is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . L is set
L is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
C '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((C '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
J is Element of Y
EqClass (J,(((C '/\' D) '/\' E) '/\' F)) is Element of ((C '/\' D) '/\' E) '/\' F
M is Element of Y
EqClass (M,(((C '/\' D) '/\' E) '/\' F)) is Element of ((C '/\' D) '/\' E) '/\' F
EqClass (M,(CompF (A,G))) is Element of CompF (A,G)
EqClass (J,(CompF (B,G))) is Element of CompF (B,G)
EqClass (M,B) is Element of B
B .--> (EqClass (M,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (M,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (M,B))}) Element of bool [:{B},{(EqClass (M,B))}:]
{(EqClass (M,B))} is non empty set
[:{B},{(EqClass (M,B))}:] is non empty set
bool [:{B},{(EqClass (M,B))}:] is non empty set
EqClass (M,C) is Element of C
C .--> (EqClass (M,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (M,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (M,C))}) Element of bool [:{C},{(EqClass (M,C))}:]
{(EqClass (M,C))} is non empty set
[:{C},{(EqClass (M,C))}:] is non empty set
bool [:{C},{(EqClass (M,C))}:] is non empty set
(B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (M,D) is Element of D
D .--> (EqClass (M,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (M,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (M,D))}) Element of bool [:{D},{(EqClass (M,D))}:]
{(EqClass (M,D))} is non empty set
[:{D},{(EqClass (M,D))}:] is non empty set
bool [:{D},{(EqClass (M,D))}:] is non empty set
((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (M,E) is Element of E
E .--> (EqClass (M,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (M,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (M,E))}) Element of bool [:{E},{(EqClass (M,E))}:]
{(EqClass (M,E))} is non empty set
[:{E},{(EqClass (M,E))}:] is non empty set
bool [:{E},{(EqClass (M,E))}:] is non empty set
(((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (M,F) is Element of F
F .--> (EqClass (M,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (M,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (M,F))}) Element of bool [:{F},{(EqClass (M,F))}:]
{(EqClass (M,F))} is non empty set
[:{F},{(EqClass (M,F))}:] is non empty set
bool [:{F},{(EqClass (M,F))}:] is non empty set
((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (J,A) is Element of A
A .--> (EqClass (J,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (J,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (J,A))}) Element of bool [:{A},{(EqClass (J,A))}:]
{(EqClass (J,A))} is non empty set
[:{A},{(EqClass (J,A))}:] is non empty set
bool [:{A},{(EqClass (J,A))}:] is non empty set
(((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A))) is Relation-like bool (bool Y) -defined Function-like set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . A is set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
EqClass (M,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
A '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
A '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(A '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
A '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(A '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((A '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
EqClass (M,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (M,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (M,F)) is Element of bool Y
EqClass (M,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (M,((B '/\' C) '/\' D))) /\ (EqClass (M,E)) is Element of bool Y
((EqClass (M,((B '/\' C) '/\' D))) /\ (EqClass (M,E))) /\ (EqClass (M,F)) is Element of bool Y
EqClass (M,(B '/\' C)) is Element of B '/\' C
(EqClass (M,(B '/\' C))) /\ (EqClass (M,D)) is Element of bool Y
((EqClass (M,(B '/\' C))) /\ (EqClass (M,D))) /\ (EqClass (M,E)) is Element of bool Y
(((EqClass (M,(B '/\' C))) /\ (EqClass (M,D))) /\ (EqClass (M,E))) /\ (EqClass (M,F)) is Element of bool Y
(EqClass (M,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (J,A)) is Element of bool Y
(EqClass (M,B)) /\ (EqClass (M,C)) is Element of bool Y
((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D)) is Element of bool Y
(((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D))) /\ (EqClass (M,E)) is Element of bool Y
((((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D))) /\ (EqClass (M,E))) /\ (EqClass (M,F)) is Element of bool Y
(((((EqClass (M,B)) /\ (EqClass (M,C))) /\ (EqClass (M,D))) /\ (EqClass (M,E))) /\ (EqClass (M,F))) /\ (EqClass (J,A)) is Element of bool Y
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . B is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . F is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . E is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . D is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . C is set
rng ((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) is set
{(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . A),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . B),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . C),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . D),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . E),(((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . F)} is non empty set
GG is set
dom ((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) is set
GG is Element of bool (bool Y)
Intersect GG is Element of bool Y
meet (rng ((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A))))) is set
I is set
((((((B .--> (EqClass (M,B))) +* (C .--> (EqClass (M,C)))) +* (D .--> (EqClass (M,D)))) +* (E .--> (EqClass (M,E)))) +* (F .--> (EqClass (M,F)))) +* (A .--> (EqClass (J,A)))) . I is set
I is set
HH is set
FF is Element of Y
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((B '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
EqClass (M,(((B '/\' (C '/\' D)) '/\' E) '/\' F)) is Element of ((B '/\' (C '/\' D)) '/\' E) '/\' F
B '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(B '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
EqClass (M,((B '/\' ((C '/\' D) '/\' E)) '/\' F)) is Element of (B '/\' ((C '/\' D) '/\' E)) '/\' F
B '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
EqClass (M,(B '/\' (((C '/\' D) '/\' E) '/\' F))) is Element of B '/\' (((C '/\' D) '/\' E) '/\' F)
EqClass (FF,(((C '/\' D) '/\' E) '/\' F)) is Element of ((C '/\' D) '/\' E) '/\' F
(EqClass (J,A)) /\ (EqClass (FF,(((C '/\' D) '/\' E) '/\' F))) is Element of bool Y
INTERSECTION (A,(((C '/\' D) '/\' E) '/\' F)) is set
(INTERSECTION (A,(((C '/\' D) '/\' E) '/\' F))) \ {{}} is Element of bool (INTERSECTION (A,(((C '/\' D) '/\' E) '/\' F)))
bool (INTERSECTION (A,(((C '/\' D) '/\' E) '/\' F))) is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
G \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E,F,J} is non empty set
{A} \/ {B,C,D,E,F,J} is non empty set
({A} \/ {B,C,D,E,F,J}) \ {A} is Element of bool ({A} \/ {B,C,D,E,F,J})
bool ({A} \/ {B,C,D,E,F,J}) is non empty set
{D,E} is non empty set
{D,E} \ {A} is Element of bool {D,E}
bool {D,E} is non empty set
{B,C,D,E,F,J} \ {A} is Element of bool {B,C,D,E,F,J}
bool {B,C,D,E,F,J} is non empty set
{B} is non empty Element of bool (PARTITIONS Y)
{C,D,E,F,J} is non empty set
{B} \/ {C,D,E,F,J} is non empty set
({B} \/ {C,D,E,F,J}) \ {A} is Element of bool ({B} \/ {C,D,E,F,J})
bool ({B} \/ {C,D,E,F,J}) is non empty set
{B} \ {A} is Element of bool (PARTITIONS Y)
{C,D,E,F,J} \ {A} is Element of bool {C,D,E,F,J}
bool {C,D,E,F,J} is non empty set
({B} \ {A}) \/ ({C,D,E,F,J} \ {A}) is set
{B} \/ ({C,D,E,F,J} \ {A}) is non empty set
{C} is non empty Element of bool (PARTITIONS Y)
{D,E,F,J} is non empty set
{C} \/ {D,E,F,J} is non empty set
({C} \/ {D,E,F,J}) \ {A} is Element of bool ({C} \/ {D,E,F,J})
bool ({C} \/ {D,E,F,J}) is non empty set
{B} \/ (({C} \/ {D,E,F,J}) \ {A}) is non empty set
{C} \ {A} is Element of bool (PARTITIONS Y)
{D,E,F,J} \ {A} is Element of bool {D,E,F,J}
bool {D,E,F,J} is non empty set
({C} \ {A}) \/ ({D,E,F,J} \ {A}) is set
{B} \/ (({C} \ {A}) \/ ({D,E,F,J} \ {A})) is non empty set
{F,J} is non empty set
{D,E} \/ {F,J} is non empty set
({D,E} \/ {F,J}) \ {A} is Element of bool ({D,E} \/ {F,J})
bool ({D,E} \/ {F,J}) is non empty set
({C} \ {A}) \/ (({D,E} \/ {F,J}) \ {A}) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \/ {F,J}) \ {A})) is non empty set
{F,J} \ {A} is Element of bool {F,J}
bool {F,J} is non empty set
({D,E} \ {A}) \/ ({F,J} \ {A}) is set
({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F,J} \ {A})) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F,J} \ {A}))) is non empty set
({C} \ {A}) \/ ({D,E} \/ {F,J}) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ {F,J})) is non empty set
{C} \/ ({D,E} \/ {F,J}) is non empty set
{B} \/ ({C} \/ ({D,E} \/ {F,J})) is non empty set
{B} \/ ({C} \/ {D,E,F,J}) is non empty set
{A} \ {A} is Element of bool (PARTITIONS Y)
({A} \ {A}) \/ {B,C,D,E,F,J} is non empty set
{} \/ {B,C,D,E,F,J} is non empty set
'/\' (G \ {A}) is non empty with_non-empty_elements a_partition of Y
M is set
N is Relation-like Function-like set
dom N is set
rng N is set
z is Element of bool (bool Y)
Intersect z is Element of bool Y
N . C is set
N . B is set
(N . B) /\ (N . C) is set
N . D is set
((N . B) /\ (N . C)) /\ (N . D) is set
N . E is set
INTERSECTION (B,C) is set
meet (rng N) is set
N . F is set
(((N . B) /\ (N . C)) /\ (N . D)) /\ (N . E) is set
((((N . B) /\ (N . C)) /\ (N . D)) /\ (N . E)) /\ (N . F) is set
N . J is set
(((((N . B) /\ (N . C)) /\ (N . D)) /\ (N . E)) /\ (N . F)) /\ (N . J) is set
I is set
{(N . B),(N . C),(N . D),(N . E),(N . F),(N . J)} is non empty set
I is set
HH is set
N . HH is set
I is set
HH is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J) is set
(INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) \ {{}} is Element of bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J))
bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) is non empty set
M is set
INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J) is set
(INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) \ {{}} is Element of bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J))
bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) is non empty set
N is set
z is set
N /\ z is set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
u is set
h is set
u /\ h is set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
L is set
GG is set
L /\ GG is set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
I is set
HH is set
I /\ HH is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
FF is set
m is set
FF /\ m is set
B .--> FF is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> FF is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{FF}) Element of bool [:{B},{FF}:]
{FF} is non empty set
[:{B},{FF}:] is non empty set
bool [:{B},{FF}:] is non empty set
C .--> m is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> m is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{m}) Element of bool [:{C},{m}:]
{m} is non empty set
[:{C},{m}:] is non empty set
bool [:{C},{m}:] is non empty set
(B .--> FF) +* (C .--> m) is Relation-like bool (bool Y) -defined Function-like set
D .--> HH is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> HH is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{HH}) Element of bool [:{D},{HH}:]
{HH} is non empty set
[:{D},{HH}:] is non empty set
bool [:{D},{HH}:] is non empty set
((B .--> FF) +* (C .--> m)) +* (D .--> HH) is Relation-like bool (bool Y) -defined Function-like set
E .--> GG is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> GG is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{GG}) Element of bool [:{E},{GG}:]
{GG} is non empty set
[:{E},{GG}:] is non empty set
bool [:{E},{GG}:] is non empty set
(((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG) is Relation-like bool (bool Y) -defined Function-like set
F .--> h is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> h is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{h}) Element of bool [:{F},{h}:]
{h} is non empty set
[:{F},{h}:] is non empty set
bool [:{F},{h}:] is non empty set
((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h) is Relation-like bool (bool Y) -defined Function-like set
J .--> z is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined Function-like one-to-one set
{J} is non empty set
{J} --> z is non empty Relation-like {J} -defined Function-like constant V17({J}) V21({J},{z}) Element of bool [:{J},{z}:]
{z} is non empty set
[:{J},{z}:] is non empty set
bool [:{J},{z}:] is non empty set
(((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z) is Relation-like bool (bool Y) -defined Function-like set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . B is set
dom ((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) is set
{J,B,C,D,E,F} is non empty set
{J} is non empty Element of bool (PARTITIONS Y)
{B,C,D,E,F} is non empty set
{J} \/ {B,C,D,E,F} is non empty set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . D is set
rng ((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) is set
p is set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . p is set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . E is set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . C is set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . F is set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . J is set
{(((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . B),(((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . C),(((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . D),(((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . E),(((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . F),(((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . J)} is non empty set
p is set
K is set
((((((B .--> FF) +* (C .--> m)) +* (D .--> HH)) +* (E .--> GG)) +* (F .--> h)) +* (J .--> z)) . K is set
p is set
p is set
p is Element of bool (bool Y)
Intersect p is Element of bool Y
d is set
b is set
K is Relation-like Function-like set
K . D is set
(FF /\ m) /\ GG is set
HH /\ ((FF /\ m) /\ GG) is set
(HH /\ ((FF /\ m) /\ GG)) /\ h is set
((HH /\ ((FF /\ m) /\ GG)) /\ h) /\ z is set
((FF /\ m) /\ GG) /\ h is set
HH /\ (((FF /\ m) /\ GG) /\ h) is set
(HH /\ (((FF /\ m) /\ GG) /\ h)) /\ z is set
(((FF /\ m) /\ GG) /\ h) /\ z is set
HH /\ ((((FF /\ m) /\ GG) /\ h) /\ z) is set
K is Relation-like Function-like set
K . B is set
HH /\ FF is set
m /\ (HH /\ FF) is set
(m /\ (HH /\ FF)) /\ GG is set
((m /\ (HH /\ FF)) /\ GG) /\ h is set
(((m /\ (HH /\ FF)) /\ GG) /\ h) /\ z is set
(HH /\ FF) /\ GG is set
m /\ ((HH /\ FF) /\ GG) is set
(m /\ ((HH /\ FF) /\ GG)) /\ h is set
((m /\ ((HH /\ FF) /\ GG)) /\ h) /\ z is set
HH /\ GG is set
(HH /\ GG) /\ FF is set
m /\ ((HH /\ GG) /\ FF) is set
(m /\ ((HH /\ GG) /\ FF)) /\ h is set
((m /\ ((HH /\ GG) /\ FF)) /\ h) /\ z is set
((HH /\ GG) /\ FF) /\ h is set
m /\ (((HH /\ GG) /\ FF) /\ h) is set
(m /\ (((HH /\ GG) /\ FF) /\ h)) /\ z is set
(((HH /\ GG) /\ FF) /\ h) /\ z is set
m /\ ((((HH /\ GG) /\ FF) /\ h) /\ z) is set
h /\ FF is set
(HH /\ GG) /\ (h /\ FF) is set
((HH /\ GG) /\ (h /\ FF)) /\ z is set
m /\ (((HH /\ GG) /\ (h /\ FF)) /\ z) is set
(h /\ FF) /\ z is set
(HH /\ GG) /\ ((h /\ FF) /\ z) is set
m /\ ((HH /\ GG) /\ ((h /\ FF) /\ z)) is set
z /\ FF is set
h /\ (z /\ FF) is set
(HH /\ GG) /\ (h /\ (z /\ FF)) is set
m /\ ((HH /\ GG) /\ (h /\ (z /\ FF))) is set
m /\ (HH /\ GG) is set
(m /\ (HH /\ GG)) /\ (h /\ (z /\ FF)) is set
(m /\ (HH /\ GG)) /\ h is set
((m /\ (HH /\ GG)) /\ h) /\ (z /\ FF) is set
((m /\ (HH /\ GG)) /\ h) /\ z is set
(((m /\ (HH /\ GG)) /\ h) /\ z) /\ FF is set
K is Relation-like Function-like set
K . C is set
HH /\ FF is set
m /\ (HH /\ FF) is set
(m /\ (HH /\ FF)) /\ GG is set
((m /\ (HH /\ FF)) /\ GG) /\ h is set
(((m /\ (HH /\ FF)) /\ GG) /\ h) /\ z is set
(HH /\ FF) /\ GG is set
m /\ ((HH /\ FF) /\ GG) is set
(m /\ ((HH /\ FF) /\ GG)) /\ h is set
((m /\ ((HH /\ FF) /\ GG)) /\ h) /\ z is set
HH /\ GG is set
(HH /\ GG) /\ FF is set
m /\ ((HH /\ GG) /\ FF) is set
(m /\ ((HH /\ GG) /\ FF)) /\ h is set
((m /\ ((HH /\ GG) /\ FF)) /\ h) /\ z is set
((HH /\ GG) /\ FF) /\ h is set
m /\ (((HH /\ GG) /\ FF) /\ h) is set
(m /\ (((HH /\ GG) /\ FF) /\ h)) /\ z is set
(((HH /\ GG) /\ FF) /\ h) /\ z is set
m /\ ((((HH /\ GG) /\ FF) /\ h) /\ z) is set
K is Relation-like Function-like set
K . E is set
(FF /\ m) /\ HH is set
h /\ GG is set
((FF /\ m) /\ HH) /\ (h /\ GG) is set
(((FF /\ m) /\ HH) /\ (h /\ GG)) /\ z is set
(h /\ GG) /\ z is set
((FF /\ m) /\ HH) /\ ((h /\ GG) /\ z) is set
h /\ z is set
(h /\ z) /\ GG is set
((FF /\ m) /\ HH) /\ ((h /\ z) /\ GG) is set
((FF /\ m) /\ HH) /\ (h /\ z) is set
(((FF /\ m) /\ HH) /\ (h /\ z)) /\ GG is set
K is Relation-like Function-like set
K . F is set
(FF /\ m) /\ HH is set
((FF /\ m) /\ HH) /\ GG is set
(((FF /\ m) /\ HH) /\ GG) /\ z is set
((((FF /\ m) /\ HH) /\ GG) /\ z) /\ h is set
K is Relation-like Function-like set
K . J is set
K is Relation-like Function-like set
K . D is set
K . B is set
K . C is set
K . E is set
K . F is set
K . J is set
K is Relation-like Function-like set
K . D is set
K . B is set
K . C is set
K . E is set
K . F is set
K . J is set
meet p is Element of bool Y
K is Relation-like Function-like set
rng K is set
meet (rng K) is set
d is set
K . C is set
K . B is set
K . D is set
(FF /\ m) /\ HH is set
K . E is set
((FF /\ m) /\ HH) /\ GG is set
K . F is set
(((FF /\ m) /\ HH) /\ GG) /\ h is set
K . J is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E,F,J} is non empty set
{A,B} \/ {C,D,E,F,J} is non empty set
{B,A,C,D,E,F,J} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
CompF (C,G) is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
((((A '/\' B) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F,J} is non empty set
{A,B,C} \/ {D,E,F,J} is non empty set
{A} is non empty Element of bool (PARTITIONS Y)
{B,C} is non empty set
{A} \/ {B,C} is non empty set
({A} \/ {B,C}) \/ {D,E,F,J} is non empty set
{A,C,B} is non empty set
{A,C,B} \/ {D,E,F,J} is non empty set
{A,C} is non empty set
{B} is non empty Element of bool (PARTITIONS Y)
{A,C} \/ {B} is non empty set
({A,C} \/ {B}) \/ {D,E,F,J} is non empty set
{C,A,B} is non empty set
{C,A,B} \/ {D,E,F,J} is non empty set
{C,A,B,D,E,F,J} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
CompF (D,G) is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
((((A '/\' B) '/\' C) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E,F,J} is non empty set
{A,B} \/ {C,D,E,F,J} is non empty set
{C,D} is non empty set
{E,F,J} is non empty set
{C,D} \/ {E,F,J} is non empty set
{A,B} \/ ({C,D} \/ {E,F,J}) is non empty set
{D,C,E,F,J} is non empty set
{A,B} \/ {D,C,E,F,J} is non empty set
{A,B,D,C,E,F,J} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
CompF (E,G) is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
((((A '/\' B) '/\' C) '/\' D) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F,J} is non empty set
{A,B,C} \/ {D,E,F,J} is non empty set
{D,E} is non empty set
{F,J} is non empty set
{D,E} \/ {F,J} is non empty set
{A,B,C} \/ ({D,E} \/ {F,J}) is non empty set
{E,D,F,J} is non empty set
{A,B,C} \/ {E,D,F,J} is non empty set
{A,B,C,E,D,F,J} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
CompF (F,G) is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
{E,F,J} is non empty set
{A,B,C,D} \/ {E,F,J} is non empty set
{F,E,J} is non empty set
{A,B,C,D} \/ {F,E,J} is non empty set
{A,B,C,D,F,E,J} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
CompF (J,G) is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
{F,J} is non empty set
{A,B,C,D,E} \/ {F,J} is non empty set
{A,B,C,D,E,J,F} is non empty set
Y is set
G is set
A is set
B is set
C is set
D is set
E is set
F is Relation-like Function-like set
F . Y is set
F . G is set
F . A is set
F . B is set
F . C is set
F . D is set
F . E is set
M is set
G .--> M is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> M is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{M}) Element of bool [:{G},{M}:]
{M} is non empty set
[:{G},{M}:] is non empty set
bool [:{G},{M}:] is non empty set
N is set
A .--> N is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> N is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{N}) Element of bool [:{A},{N}:]
{N} is non empty set
[:{A},{N}:] is non empty set
bool [:{A},{N}:] is non empty set
(G .--> M) +* (A .--> N) is Relation-like Function-like set
z is set
B .--> z is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> z is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{z}) Element of bool [:{B},{z}:]
{z} is non empty set
[:{B},{z}:] is non empty set
bool [:{B},{z}:] is non empty set
((G .--> M) +* (A .--> N)) +* (B .--> z) is Relation-like Function-like set
u is set
C .--> u is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> u is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{u}) Element of bool [:{C},{u}:]
{u} is non empty set
[:{C},{u}:] is non empty set
bool [:{C},{u}:] is non empty set
(((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u) is Relation-like Function-like set
h is set
D .--> h is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> h is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{h}) Element of bool [:{D},{h}:]
{h} is non empty set
[:{D},{h}:] is non empty set
bool [:{D},{h}:] is non empty set
((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h) is Relation-like Function-like set
L is set
E .--> L is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> L is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{L}) Element of bool [:{E},{L}:]
{L} is non empty set
[:{E},{L}:] is non empty set
bool [:{E},{L}:] is non empty set
(((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L) is Relation-like Function-like set
J is set
Y .--> J is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> J is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{J}) Element of bool [:{Y},{J}:]
{J} is non empty set
[:{Y},{J}:] is non empty set
bool [:{Y},{J}:] is non empty set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) +* (Y .--> J) is Relation-like Function-like set
dom (Y .--> J) is set
(Y .--> J) . Y is set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) . E is set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) . D is set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) . C is set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) . B is set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) . A is set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) . G is set
G is set
A is set
B is set
C is set
D is set
E is set
Y is set
{Y,G,A,B,C,D,E} is non empty set
F is Relation-like Function-like set
dom F is set
M is set
G .--> M is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> M is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{M}) Element of bool [:{G},{M}:]
{M} is non empty set
[:{G},{M}:] is non empty set
bool [:{G},{M}:] is non empty set
N is set
A .--> N is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> N is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{N}) Element of bool [:{A},{N}:]
{N} is non empty set
[:{A},{N}:] is non empty set
bool [:{A},{N}:] is non empty set
(G .--> M) +* (A .--> N) is Relation-like Function-like set
z is set
B .--> z is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> z is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{z}) Element of bool [:{B},{z}:]
{z} is non empty set
[:{B},{z}:] is non empty set
bool [:{B},{z}:] is non empty set
((G .--> M) +* (A .--> N)) +* (B .--> z) is Relation-like Function-like set
u is set
C .--> u is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> u is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{u}) Element of bool [:{C},{u}:]
{u} is non empty set
[:{C},{u}:] is non empty set
bool [:{C},{u}:] is non empty set
(((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u) is Relation-like Function-like set
h is set
D .--> h is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> h is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{h}) Element of bool [:{D},{h}:]
{h} is non empty set
[:{D},{h}:] is non empty set
bool [:{D},{h}:] is non empty set
((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h) is Relation-like Function-like set
L is set
E .--> L is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> L is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{L}) Element of bool [:{E},{L}:]
{L} is non empty set
[:{E},{L}:] is non empty set
bool [:{E},{L}:] is non empty set
(((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L) is Relation-like Function-like set
J is set
Y .--> J is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> J is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{J}) Element of bool [:{Y},{J}:]
{J} is non empty set
[:{Y},{J}:] is non empty set
bool [:{Y},{J}:] is non empty set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) +* (Y .--> J) is Relation-like Function-like set
dom (Y .--> J) is set
dom ((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) is set
(dom ((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L))) \/ (dom (Y .--> J)) is set
{E,G,A,B,C,D} is non empty set
{E,G,A,B,C,D} \/ (dom (Y .--> J)) is non empty set
{G,A,B,C,D} is non empty set
{G,A,B,C,D} \/ {E} is non empty set
({G,A,B,C,D} \/ {E}) \/ {Y} is non empty set
{G,A,B,C,D,E} is non empty set
{G,A,B,C,D,E} \/ {Y} is non empty set
G is set
A is set
B is set
C is set
D is set
E is set
Y is set
F is Relation-like Function-like set
rng F is set
F . Y is set
F . G is set
F . A is set
F . B is set
F . C is set
F . D is set
F . E is set
{(F . Y),(F . G),(F . A),(F . B),(F . C),(F . D),(F . E)} is non empty set
M is set
G .--> M is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> M is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{M}) Element of bool [:{G},{M}:]
{M} is non empty set
[:{G},{M}:] is non empty set
bool [:{G},{M}:] is non empty set
N is set
A .--> N is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> N is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{N}) Element of bool [:{A},{N}:]
{N} is non empty set
[:{A},{N}:] is non empty set
bool [:{A},{N}:] is non empty set
(G .--> M) +* (A .--> N) is Relation-like Function-like set
z is set
B .--> z is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> z is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{z}) Element of bool [:{B},{z}:]
{z} is non empty set
[:{B},{z}:] is non empty set
bool [:{B},{z}:] is non empty set
((G .--> M) +* (A .--> N)) +* (B .--> z) is Relation-like Function-like set
u is set
C .--> u is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> u is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{u}) Element of bool [:{C},{u}:]
{u} is non empty set
[:{C},{u}:] is non empty set
bool [:{C},{u}:] is non empty set
(((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u) is Relation-like Function-like set
h is set
D .--> h is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> h is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{h}) Element of bool [:{D},{h}:]
{h} is non empty set
[:{D},{h}:] is non empty set
bool [:{D},{h}:] is non empty set
((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h) is Relation-like Function-like set
L is set
E .--> L is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> L is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{L}) Element of bool [:{E},{L}:]
{L} is non empty set
[:{E},{L}:] is non empty set
bool [:{E},{L}:] is non empty set
(((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L) is Relation-like Function-like set
J is set
Y .--> J is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> J is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{J}) Element of bool [:{Y},{J}:]
{J} is non empty set
[:{Y},{J}:] is non empty set
bool [:{Y},{J}:] is non empty set
((((((G .--> M) +* (A .--> N)) +* (B .--> z)) +* (C .--> u)) +* (D .--> h)) +* (E .--> L)) +* (Y .--> J) is Relation-like Function-like set
dom F is set
{Y,G,A,B,C,D,E} is non empty set
GG is set
I is set
F . I is set
GG is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
N is Element of Y
EqClass (N,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)) is Element of ((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J
M is Element of Y
EqClass (M,A) is Element of A
EqClass (N,B) is Element of B
B .--> (EqClass (N,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (N,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (N,B))}) Element of bool [:{B},{(EqClass (N,B))}:]
{(EqClass (N,B))} is non empty set
[:{B},{(EqClass (N,B))}:] is non empty set
bool [:{B},{(EqClass (N,B))}:] is non empty set
EqClass (N,C) is Element of C
C .--> (EqClass (N,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (N,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (N,C))}) Element of bool [:{C},{(EqClass (N,C))}:]
{(EqClass (N,C))} is non empty set
[:{C},{(EqClass (N,C))}:] is non empty set
bool [:{C},{(EqClass (N,C))}:] is non empty set
(B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,D) is Element of D
D .--> (EqClass (N,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (N,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (N,D))}) Element of bool [:{D},{(EqClass (N,D))}:]
{(EqClass (N,D))} is non empty set
[:{D},{(EqClass (N,D))}:] is non empty set
bool [:{D},{(EqClass (N,D))}:] is non empty set
((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,E) is Element of E
E .--> (EqClass (N,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (N,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (N,E))}) Element of bool [:{E},{(EqClass (N,E))}:]
{(EqClass (N,E))} is non empty set
[:{E},{(EqClass (N,E))}:] is non empty set
bool [:{E},{(EqClass (N,E))}:] is non empty set
(((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,F) is Element of F
F .--> (EqClass (N,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (N,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (N,F))}) Element of bool [:{F},{(EqClass (N,F))}:]
{(EqClass (N,F))} is non empty set
[:{F},{(EqClass (N,F))}:] is non empty set
bool [:{F},{(EqClass (N,F))}:] is non empty set
((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,J) is Element of J
J .--> (EqClass (N,J)) is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined J -valued Function-like one-to-one set
{J} is non empty set
{J} --> (EqClass (N,J)) is non empty Relation-like {J} -defined J -valued Function-like constant V17({J}) V21({J},{(EqClass (N,J))}) Element of bool [:{J},{(EqClass (N,J))}:]
{(EqClass (N,J))} is non empty set
[:{J},{(EqClass (N,J))}:] is non empty set
bool [:{J},{(EqClass (N,J))}:] is non empty set
(((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J))) is Relation-like bool (bool Y) -defined Function-like set
A .--> (EqClass (M,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (M,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (M,A))}) Element of bool [:{A},{(EqClass (M,A))}:]
{(EqClass (M,A))} is non empty set
[:{A},{(EqClass (M,A))}:] is non empty set
bool [:{A},{(EqClass (M,A))}:] is non empty set
((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A))) is Relation-like bool (bool Y) -defined Function-like set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . A is set
u is set
EqClass (N,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
(EqClass (N,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (N,J)) is Element of bool Y
EqClass (N,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (N,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (N,F)) is Element of bool Y
((EqClass (N,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
EqClass (N,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (N,((B '/\' C) '/\' D))) /\ (EqClass (N,E)) is Element of bool Y
((EqClass (N,((B '/\' C) '/\' D))) /\ (EqClass (N,E))) /\ (EqClass (N,F)) is Element of bool Y
(((EqClass (N,((B '/\' C) '/\' D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
EqClass (N,(B '/\' C)) is Element of B '/\' C
(EqClass (N,(B '/\' C))) /\ (EqClass (N,D)) is Element of bool Y
((EqClass (N,(B '/\' C))) /\ (EqClass (N,D))) /\ (EqClass (N,E)) is Element of bool Y
(((EqClass (N,(B '/\' C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F)) is Element of bool Y
((((EqClass (N,(B '/\' C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
h is set
u /\ h is set
(EqClass (N,B)) /\ (EqClass (N,C)) is Element of bool Y
((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D)) is Element of bool Y
(((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E)) is Element of bool Y
((((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F)) is Element of bool Y
(((((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
((((((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J))) /\ (EqClass (M,A)) is Element of bool Y
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . B is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . F is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . E is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . J is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . D is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . C is set
rng (((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) is set
{((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . A),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . B),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . C),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . D),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . E),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . F),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . J)} is non empty set
L is set
dom (((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) is set
L is Element of bool (bool Y)
Intersect L is Element of bool Y
meet (rng (((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A))))) is set
GG is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . GG is set
GG is set
(EqClass (N,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) /\ (EqClass (M,A)) is Element of bool Y
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
C '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((C '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((C '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
M is Element of Y
EqClass (M,((((C '/\' D) '/\' E) '/\' F) '/\' J)) is Element of (((C '/\' D) '/\' E) '/\' F) '/\' J
N is Element of Y
EqClass (N,((((C '/\' D) '/\' E) '/\' F) '/\' J)) is Element of (((C '/\' D) '/\' E) '/\' F) '/\' J
EqClass (N,(CompF (A,G))) is Element of CompF (A,G)
EqClass (M,(CompF (B,G))) is Element of CompF (B,G)
EqClass (N,B) is Element of B
B .--> (EqClass (N,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (N,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (N,B))}) Element of bool [:{B},{(EqClass (N,B))}:]
{(EqClass (N,B))} is non empty set
[:{B},{(EqClass (N,B))}:] is non empty set
bool [:{B},{(EqClass (N,B))}:] is non empty set
EqClass (N,C) is Element of C
C .--> (EqClass (N,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (N,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (N,C))}) Element of bool [:{C},{(EqClass (N,C))}:]
{(EqClass (N,C))} is non empty set
[:{C},{(EqClass (N,C))}:] is non empty set
bool [:{C},{(EqClass (N,C))}:] is non empty set
(B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,D) is Element of D
D .--> (EqClass (N,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (N,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (N,D))}) Element of bool [:{D},{(EqClass (N,D))}:]
{(EqClass (N,D))} is non empty set
[:{D},{(EqClass (N,D))}:] is non empty set
bool [:{D},{(EqClass (N,D))}:] is non empty set
((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,E) is Element of E
E .--> (EqClass (N,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (N,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (N,E))}) Element of bool [:{E},{(EqClass (N,E))}:]
{(EqClass (N,E))} is non empty set
[:{E},{(EqClass (N,E))}:] is non empty set
bool [:{E},{(EqClass (N,E))}:] is non empty set
(((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,F) is Element of F
F .--> (EqClass (N,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (N,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (N,F))}) Element of bool [:{F},{(EqClass (N,F))}:]
{(EqClass (N,F))} is non empty set
[:{F},{(EqClass (N,F))}:] is non empty set
bool [:{F},{(EqClass (N,F))}:] is non empty set
((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,J) is Element of J
J .--> (EqClass (N,J)) is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined J -valued Function-like one-to-one set
{J} is non empty set
{J} --> (EqClass (N,J)) is non empty Relation-like {J} -defined J -valued Function-like constant V17({J}) V21({J},{(EqClass (N,J))}) Element of bool [:{J},{(EqClass (N,J))}:]
{(EqClass (N,J))} is non empty set
[:{J},{(EqClass (N,J))}:] is non empty set
bool [:{J},{(EqClass (N,J))}:] is non empty set
(((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (M,A) is Element of A
A .--> (EqClass (M,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (M,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (M,A))}) Element of bool [:{A},{(EqClass (M,A))}:]
{(EqClass (M,A))} is non empty set
[:{A},{(EqClass (M,A))}:] is non empty set
bool [:{A},{(EqClass (M,A))}:] is non empty set
((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A))) is Relation-like bool (bool Y) -defined Function-like set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . A is set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
EqClass (N,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)) is Element of ((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J
h is set
EqClass (N,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
(EqClass (N,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (N,J)) is Element of bool Y
EqClass (N,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (N,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (N,F)) is Element of bool Y
((EqClass (N,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
EqClass (N,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (N,((B '/\' C) '/\' D))) /\ (EqClass (N,E)) is Element of bool Y
((EqClass (N,((B '/\' C) '/\' D))) /\ (EqClass (N,E))) /\ (EqClass (N,F)) is Element of bool Y
(((EqClass (N,((B '/\' C) '/\' D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
EqClass (N,(B '/\' C)) is Element of B '/\' C
(EqClass (N,(B '/\' C))) /\ (EqClass (N,D)) is Element of bool Y
((EqClass (N,(B '/\' C))) /\ (EqClass (N,D))) /\ (EqClass (N,E)) is Element of bool Y
(((EqClass (N,(B '/\' C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F)) is Element of bool Y
((((EqClass (N,(B '/\' C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
L is set
h /\ L is set
(EqClass (N,B)) /\ (EqClass (N,C)) is Element of bool Y
((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D)) is Element of bool Y
(((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E)) is Element of bool Y
((((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F)) is Element of bool Y
(((((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J)) is Element of bool Y
((((((EqClass (N,B)) /\ (EqClass (N,C))) /\ (EqClass (N,D))) /\ (EqClass (N,E))) /\ (EqClass (N,F))) /\ (EqClass (N,J))) /\ (EqClass (M,A)) is Element of bool Y
GG is set
A '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J) is non empty with_non-empty_elements a_partition of Y
A '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
(A '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J is non empty with_non-empty_elements a_partition of Y
A '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(A '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
((A '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
A '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(A '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((A '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((A '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . B is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . F is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . E is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . J is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . D is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . C is set
rng (((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) is set
{((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . A),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . B),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . C),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . D),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . E),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . F),((((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . J)} is non empty set
I is set
dom (((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) is set
I is Element of bool (bool Y)
Intersect I is Element of bool Y
meet (rng (((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A))))) is set
HH is set
(((((((B .--> (EqClass (N,B))) +* (C .--> (EqClass (N,C)))) +* (D .--> (EqClass (N,D)))) +* (E .--> (EqClass (N,E)))) +* (F .--> (EqClass (N,F)))) +* (J .--> (EqClass (N,J)))) +* (A .--> (EqClass (M,A)))) . HH is set
HH is set
FF is set
INTERSECTION (A,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)) is set
(INTERSECTION (A,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) \ {{}} is Element of bool (INTERSECTION (A,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)))
bool (INTERSECTION (A,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) is non empty set
A '/\' (((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) is non empty with_non-empty_elements a_partition of Y
m is Element of Y
EqClass (m,((((C '/\' D) '/\' E) '/\' F) '/\' J)) is Element of (((C '/\' D) '/\' E) '/\' F) '/\' J
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((B '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
EqClass (N,((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J)) is Element of (((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J
B '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(B '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
EqClass (N,(((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J)) is Element of ((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J
B '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
(B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J is non empty with_non-empty_elements a_partition of Y
EqClass (N,((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J)) is Element of (B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J
B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J) is non empty with_non-empty_elements a_partition of Y
EqClass (N,(B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J))) is Element of B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)
u is set
p is set
L /\ p is set
INTERSECTION (A,((((C '/\' D) '/\' E) '/\' F) '/\' J)) is set
(INTERSECTION (A,((((C '/\' D) '/\' E) '/\' F) '/\' J))) \ {{}} is Element of bool (INTERSECTION (A,((((C '/\' D) '/\' E) '/\' F) '/\' J)))
bool (INTERSECTION (A,((((C '/\' D) '/\' E) '/\' F) '/\' J))) is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
G \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E,F,J,M} is non empty set
{A} \/ {B,C,D,E,F,J,M} is non empty set
({A} \/ {B,C,D,E,F,J,M}) \ {A} is Element of bool ({A} \/ {B,C,D,E,F,J,M})
bool ({A} \/ {B,C,D,E,F,J,M}) is non empty set
{A} \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E,F,J,M} \ {A} is Element of bool {B,C,D,E,F,J,M}
bool {B,C,D,E,F,J,M} is non empty set
({A} \ {A}) \/ ({B,C,D,E,F,J,M} \ {A}) is set
{B} is non empty Element of bool (PARTITIONS Y)
{C,D,E,F,J,M} is non empty set
{B} \/ {C,D,E,F,J,M} is non empty set
({B} \/ {C,D,E,F,J,M}) \ {A} is Element of bool ({B} \/ {C,D,E,F,J,M})
bool ({B} \/ {C,D,E,F,J,M}) is non empty set
{B} \ {A} is Element of bool (PARTITIONS Y)
{C,D,E,F,J,M} \ {A} is Element of bool {C,D,E,F,J,M}
bool {C,D,E,F,J,M} is non empty set
({B} \ {A}) \/ ({C,D,E,F,J,M} \ {A}) is set
{B} \/ ({C,D,E,F,J,M} \ {A}) is non empty set
{C} is non empty Element of bool (PARTITIONS Y)
{D,E,F,J,M} is non empty set
{C} \/ {D,E,F,J,M} is non empty set
({C} \/ {D,E,F,J,M}) \ {A} is Element of bool ({C} \/ {D,E,F,J,M})
bool ({C} \/ {D,E,F,J,M}) is non empty set
{B} \/ (({C} \/ {D,E,F,J,M}) \ {A}) is non empty set
{C} \ {A} is Element of bool (PARTITIONS Y)
{D,E,F,J,M} \ {A} is Element of bool {D,E,F,J,M}
bool {D,E,F,J,M} is non empty set
({C} \ {A}) \/ ({D,E,F,J,M} \ {A}) is set
{B} \/ (({C} \ {A}) \/ ({D,E,F,J,M} \ {A})) is non empty set
{D,E} is non empty set
{F,J,M} is non empty set
{D,E} \/ {F,J,M} is non empty set
({D,E} \/ {F,J,M}) \ {A} is Element of bool ({D,E} \/ {F,J,M})
bool ({D,E} \/ {F,J,M}) is non empty set
({C} \ {A}) \/ (({D,E} \/ {F,J,M}) \ {A}) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \/ {F,J,M}) \ {A})) is non empty set
{D,E} \ {A} is Element of bool {D,E}
bool {D,E} is non empty set
{F,J,M} \ {A} is Element of bool {F,J,M}
bool {F,J,M} is non empty set
({D,E} \ {A}) \/ ({F,J,M} \ {A}) is set
({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F,J,M} \ {A})) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F,J,M} \ {A}))) is non empty set
{D,E} \/ ({F,J,M} \ {A}) is non empty set
({C} \ {A}) \/ ({D,E} \/ ({F,J,M} \ {A})) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ ({F,J,M} \ {A}))) is non empty set
{F,J} is non empty set
{M} is non empty Element of bool (PARTITIONS Y)
{F,J} \/ {M} is non empty set
({F,J} \/ {M}) \ {A} is Element of bool ({F,J} \/ {M})
bool ({F,J} \/ {M}) is non empty set
{D,E} \/ (({F,J} \/ {M}) \ {A}) is non empty set
({C} \ {A}) \/ ({D,E} \/ (({F,J} \/ {M}) \ {A})) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ (({F,J} \/ {M}) \ {A}))) is non empty set
{F,J} \ {A} is Element of bool {F,J}
bool {F,J} is non empty set
{M} \ {A} is Element of bool (PARTITIONS Y)
({F,J} \ {A}) \/ ({M} \ {A}) is set
{D,E} \/ (({F,J} \ {A}) \/ ({M} \ {A})) is non empty set
({C} \ {A}) \/ ({D,E} \/ (({F,J} \ {A}) \/ ({M} \ {A}))) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ (({F,J} \ {A}) \/ ({M} \ {A})))) is non empty set
{F,J} \/ ({M} \ {A}) is non empty set
{D,E} \/ ({F,J} \/ ({M} \ {A})) is non empty set
({C} \ {A}) \/ ({D,E} \/ ({F,J} \/ ({M} \ {A}))) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ ({F,J} \/ ({M} \ {A})))) is non empty set
{C} \/ ({D,E} \/ ({F,J} \/ ({M} \ {A}))) is non empty set
{B} \/ ({C} \/ ({D,E} \/ ({F,J} \/ ({M} \ {A})))) is non empty set
{D,E} \/ ({F,J} \/ {M}) is non empty set
{C} \/ ({D,E} \/ ({F,J} \/ {M})) is non empty set
{B} \/ ({C} \/ ({D,E} \/ ({F,J} \/ {M}))) is non empty set
{C} \/ ({D,E} \/ {F,J,M}) is non empty set
{B} \/ ({C} \/ ({D,E} \/ {F,J,M})) is non empty set
{B} \/ ({C} \/ {D,E,F,J,M}) is non empty set
{} \/ {B,C,D,E,F,J,M} is non empty set
'/\' (G \ {A}) is non empty with_non-empty_elements a_partition of Y
N is set
z is Relation-like Function-like set
dom z is set
rng z is set
u is Element of bool (bool Y)
Intersect u is Element of bool Y
z . C is set
z . B is set
(z . B) /\ (z . C) is set
z . D is set
((z . B) /\ (z . C)) /\ (z . D) is set
z . E is set
(((z . B) /\ (z . C)) /\ (z . D)) /\ (z . E) is set
z . F is set
((((z . B) /\ (z . C)) /\ (z . D)) /\ (z . E)) /\ (z . F) is set
z . J is set
(((((z . B) /\ (z . C)) /\ (z . D)) /\ (z . E)) /\ (z . F)) /\ (z . J) is set
INTERSECTION (B,C) is set
meet (rng z) is set
z . M is set
((((((z . B) /\ (z . C)) /\ (z . D)) /\ (z . E)) /\ (z . F)) /\ (z . J)) /\ (z . M) is set
FF is set
{(z . B),(z . C),(z . D),(z . E),(z . F),(z . J),(z . M)} is non empty set
FF is set
m is set
z . m is set
FF is set
m is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J) is set
(INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) \ {{}} is Element of bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J))
bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) is non empty set
INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M) is set
(INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) \ {{}} is Element of bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M))
bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) is non empty set
N is set
INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M) is set
(INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) \ {{}} is Element of bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M))
bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) is non empty set
z is set
u is set
z /\ u is set
INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J) is set
(INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) \ {{}} is Element of bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J))
bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) is non empty set
h is set
L is set
h /\ L is set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
GG is set
I is set
GG /\ I is set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
HH is set
FF is set
HH /\ FF is set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
m is set
p is set
m /\ p is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
p is set
K is set
p /\ K is set
B .--> p is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> p is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{p}) Element of bool [:{B},{p}:]
{p} is non empty set
[:{B},{p}:] is non empty set
bool [:{B},{p}:] is non empty set
C .--> K is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> K is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{K}) Element of bool [:{C},{K}:]
{K} is non empty set
[:{C},{K}:] is non empty set
bool [:{C},{K}:] is non empty set
(B .--> p) +* (C .--> K) is Relation-like bool (bool Y) -defined Function-like set
D .--> p is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> p is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{p}) Element of bool [:{D},{p}:]
{p} is non empty set
[:{D},{p}:] is non empty set
bool [:{D},{p}:] is non empty set
((B .--> p) +* (C .--> K)) +* (D .--> p) is Relation-like bool (bool Y) -defined Function-like set
E .--> FF is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> FF is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{FF}) Element of bool [:{E},{FF}:]
{FF} is non empty set
[:{E},{FF}:] is non empty set
bool [:{E},{FF}:] is non empty set
(((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF) is Relation-like bool (bool Y) -defined Function-like set
F .--> I is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> I is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{I}) Element of bool [:{F},{I}:]
{I} is non empty set
[:{F},{I}:] is non empty set
bool [:{F},{I}:] is non empty set
((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I) is Relation-like bool (bool Y) -defined Function-like set
J .--> L is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined Function-like one-to-one set
{J} is non empty set
{J} --> L is non empty Relation-like {J} -defined Function-like constant V17({J}) V21({J},{L}) Element of bool [:{J},{L}:]
{L} is non empty set
[:{J},{L}:] is non empty set
bool [:{J},{L}:] is non empty set
(((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L) is Relation-like bool (bool Y) -defined Function-like set
M .--> u is trivial Relation-like {M} -defined bool (bool Y) -defined {M} -defined Function-like one-to-one set
{M} is non empty set
{M} --> u is non empty Relation-like {M} -defined Function-like constant V17({M}) V21({M},{u}) Element of bool [:{M},{u}:]
{u} is non empty set
[:{M},{u}:] is non empty set
bool [:{M},{u}:] is non empty set
((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u) is Relation-like bool (bool Y) -defined Function-like set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . B is set
dom (((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) is set
{M,B,C,D,E,F,J} is non empty set
{B,C,D,E,F,J} is non empty set
{M} \/ {B,C,D,E,F,J} is non empty set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . D is set
rng (((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) is set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . C is set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . E is set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . F is set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . J is set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . M is set
{((((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . B),((((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . C),((((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . D),((((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . E),((((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . F),((((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . J),((((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . M)} is non empty set
b is set
b is set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . b is set
b is set
c is set
(((((((B .--> p) +* (C .--> K)) +* (D .--> p)) +* (E .--> FF)) +* (F .--> I)) +* (J .--> L)) +* (M .--> u)) . c is set
b is set
b is Element of bool (bool Y)
Intersect b is Element of bool Y
h is set
FF is set
c is Relation-like Function-like set
c . D is set
(p /\ K) /\ FF is set
p /\ ((p /\ K) /\ FF) is set
(p /\ ((p /\ K) /\ FF)) /\ I is set
((p /\ ((p /\ K) /\ FF)) /\ I) /\ L is set
(((p /\ ((p /\ K) /\ FF)) /\ I) /\ L) /\ u is set
((p /\ K) /\ FF) /\ I is set
p /\ (((p /\ K) /\ FF) /\ I) is set
(p /\ (((p /\ K) /\ FF) /\ I)) /\ L is set
((p /\ (((p /\ K) /\ FF) /\ I)) /\ L) /\ u is set
(((p /\ K) /\ FF) /\ I) /\ L is set
p /\ ((((p /\ K) /\ FF) /\ I) /\ L) is set
(p /\ ((((p /\ K) /\ FF) /\ I) /\ L)) /\ u is set
((((p /\ K) /\ FF) /\ I) /\ L) /\ u is set
p /\ (((((p /\ K) /\ FF) /\ I) /\ L) /\ u) is set
c is Relation-like Function-like set
c . B is set
p /\ p is set
K /\ (p /\ p) is set
(K /\ (p /\ p)) /\ FF is set
((K /\ (p /\ p)) /\ FF) /\ I is set
(((K /\ (p /\ p)) /\ FF) /\ I) /\ L is set
((((K /\ (p /\ p)) /\ FF) /\ I) /\ L) /\ u is set
(p /\ p) /\ FF is set
K /\ ((p /\ p) /\ FF) is set
(K /\ ((p /\ p) /\ FF)) /\ I is set
((K /\ ((p /\ p) /\ FF)) /\ I) /\ L is set
(((K /\ ((p /\ p) /\ FF)) /\ I) /\ L) /\ u is set
p /\ FF is set
(p /\ FF) /\ p is set
K /\ ((p /\ FF) /\ p) is set
(K /\ ((p /\ FF) /\ p)) /\ I is set
((K /\ ((p /\ FF) /\ p)) /\ I) /\ L is set
(((K /\ ((p /\ FF) /\ p)) /\ I) /\ L) /\ u is set
((p /\ FF) /\ p) /\ I is set
K /\ (((p /\ FF) /\ p) /\ I) is set
(K /\ (((p /\ FF) /\ p) /\ I)) /\ L is set
((K /\ (((p /\ FF) /\ p) /\ I)) /\ L) /\ u is set
(((p /\ FF) /\ p) /\ I) /\ L is set
K /\ ((((p /\ FF) /\ p) /\ I) /\ L) is set
(K /\ ((((p /\ FF) /\ p) /\ I) /\ L)) /\ u is set
I /\ p is set
(p /\ FF) /\ (I /\ p) is set
((p /\ FF) /\ (I /\ p)) /\ L is set
K /\ (((p /\ FF) /\ (I /\ p)) /\ L) is set
(K /\ (((p /\ FF) /\ (I /\ p)) /\ L)) /\ u is set
(I /\ p) /\ L is set
(p /\ FF) /\ ((I /\ p) /\ L) is set
K /\ ((p /\ FF) /\ ((I /\ p) /\ L)) is set
(K /\ ((p /\ FF) /\ ((I /\ p) /\ L))) /\ u is set
L /\ p is set
I /\ (L /\ p) is set
(p /\ FF) /\ (I /\ (L /\ p)) is set
K /\ ((p /\ FF) /\ (I /\ (L /\ p))) is set
(K /\ ((p /\ FF) /\ (I /\ (L /\ p)))) /\ u is set
K /\ (p /\ FF) is set
(K /\ (p /\ FF)) /\ (I /\ (L /\ p)) is set
((K /\ (p /\ FF)) /\ (I /\ (L /\ p))) /\ u is set
(K /\ (p /\ FF)) /\ I is set
((K /\ (p /\ FF)) /\ I) /\ (L /\ p) is set
(((K /\ (p /\ FF)) /\ I) /\ (L /\ p)) /\ u is set
((K /\ (p /\ FF)) /\ I) /\ L is set
(((K /\ (p /\ FF)) /\ I) /\ L) /\ p is set
((((K /\ (p /\ FF)) /\ I) /\ L) /\ p) /\ u is set
(((K /\ (p /\ FF)) /\ I) /\ L) /\ u is set
((((K /\ (p /\ FF)) /\ I) /\ L) /\ u) /\ p is set
c is Relation-like Function-like set
c . C is set
p /\ p is set
K /\ (p /\ p) is set
(K /\ (p /\ p)) /\ FF is set
((K /\ (p /\ p)) /\ FF) /\ I is set
(((K /\ (p /\ p)) /\ FF) /\ I) /\ L is set
((((K /\ (p /\ p)) /\ FF) /\ I) /\ L) /\ u is set
(p /\ p) /\ FF is set
K /\ ((p /\ p) /\ FF) is set
(K /\ ((p /\ p) /\ FF)) /\ I is set
((K /\ ((p /\ p) /\ FF)) /\ I) /\ L is set
(((K /\ ((p /\ p) /\ FF)) /\ I) /\ L) /\ u is set
p /\ FF is set
(p /\ FF) /\ p is set
K /\ ((p /\ FF) /\ p) is set
(K /\ ((p /\ FF) /\ p)) /\ I is set
((K /\ ((p /\ FF) /\ p)) /\ I) /\ L is set
(((K /\ ((p /\ FF) /\ p)) /\ I) /\ L) /\ u is set
((p /\ FF) /\ p) /\ I is set
K /\ (((p /\ FF) /\ p) /\ I) is set
(K /\ (((p /\ FF) /\ p) /\ I)) /\ L is set
((K /\ (((p /\ FF) /\ p) /\ I)) /\ L) /\ u is set
(((p /\ FF) /\ p) /\ I) /\ L is set
K /\ ((((p /\ FF) /\ p) /\ I) /\ L) is set
(K /\ ((((p /\ FF) /\ p) /\ I) /\ L)) /\ u is set
((((p /\ FF) /\ p) /\ I) /\ L) /\ u is set
K /\ (((((p /\ FF) /\ p) /\ I) /\ L) /\ u) is set
c is Relation-like Function-like set
c . E is set
(p /\ K) /\ p is set
I /\ FF is set
((p /\ K) /\ p) /\ (I /\ FF) is set
(((p /\ K) /\ p) /\ (I /\ FF)) /\ L is set
((((p /\ K) /\ p) /\ (I /\ FF)) /\ L) /\ u is set
(I /\ FF) /\ L is set
((p /\ K) /\ p) /\ ((I /\ FF) /\ L) is set
(((p /\ K) /\ p) /\ ((I /\ FF) /\ L)) /\ u is set
I /\ L is set
(I /\ L) /\ FF is set
((p /\ K) /\ p) /\ ((I /\ L) /\ FF) is set
(((p /\ K) /\ p) /\ ((I /\ L) /\ FF)) /\ u is set
((p /\ K) /\ p) /\ (I /\ L) is set
(((p /\ K) /\ p) /\ (I /\ L)) /\ FF is set
((((p /\ K) /\ p) /\ (I /\ L)) /\ FF) /\ u is set
(((p /\ K) /\ p) /\ (I /\ L)) /\ u is set
((((p /\ K) /\ p) /\ (I /\ L)) /\ u) /\ FF is set
c is Relation-like Function-like set
c . F is set
(p /\ K) /\ p is set
((p /\ K) /\ p) /\ FF is set
(((p /\ K) /\ p) /\ FF) /\ L is set
((((p /\ K) /\ p) /\ FF) /\ L) /\ I is set
(((((p /\ K) /\ p) /\ FF) /\ L) /\ I) /\ u is set
((((p /\ K) /\ p) /\ FF) /\ L) /\ u is set
(((((p /\ K) /\ p) /\ FF) /\ L) /\ u) /\ I is set
c is Relation-like Function-like set
c . J is set
(p /\ K) /\ p is set
((p /\ K) /\ p) /\ FF is set
(((p /\ K) /\ p) /\ FF) /\ I is set
((((p /\ K) /\ p) /\ FF) /\ I) /\ u is set
(((((p /\ K) /\ p) /\ FF) /\ I) /\ u) /\ L is set
c is Relation-like Function-like set
c . M is set
c is Relation-like Function-like set
c . D is set
c . B is set
c . C is set
c . E is set
c . F is set
c . J is set
c . M is set
c is Relation-like Function-like set
c . D is set
c . B is set
c . C is set
c . E is set
c . F is set
c . J is set
c . M is set
meet b is Element of bool Y
c is Relation-like Function-like set
rng c is set
meet (rng c) is set
h is set
c . C is set
c . B is set
c . D is set
c . E is set
c . F is set
c . J is set
c . M is set
{(c . B),(c . C),(c . D),(c . E),(c . F),(c . J),(c . M)} is non empty set
(p /\ K) /\ p is set
((p /\ K) /\ p) /\ FF is set
(((p /\ K) /\ p) /\ FF) /\ I is set
((((p /\ K) /\ p) /\ FF) /\ I) /\ L is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
(((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E,F,J,M} is non empty set
{A,B} \/ {C,D,E,F,J,M} is non empty set
{B,A,C,D,E,F,J,M} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
CompF (C,G) is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
(((((A '/\' B) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F,J,M} is non empty set
{A,B,C} \/ {D,E,F,J,M} is non empty set
{A} is non empty Element of bool (PARTITIONS Y)
{B,C} is non empty set
{A} \/ {B,C} is non empty set
({A} \/ {B,C}) \/ {D,E,F,J,M} is non empty set
{A,C,B} is non empty set
{A,C,B} \/ {D,E,F,J,M} is non empty set
{A,C,B,D,E,F,J,M} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
CompF (D,G) is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
(((((A '/\' B) '/\' C) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E,F,J,M} is non empty set
{A,B} \/ {C,D,E,F,J,M} is non empty set
{C,D} is non empty set
{E,F,J,M} is non empty set
{C,D} \/ {E,F,J,M} is non empty set
{A,B} \/ ({C,D} \/ {E,F,J,M}) is non empty set
{D,C,E,F,J,M} is non empty set
{A,B} \/ {D,C,E,F,J,M} is non empty set
{A,B,D,C,E,F,J,M} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
CompF (E,G) is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
(((((A '/\' B) '/\' C) '/\' D) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F,J,M} is non empty set
{A,B,C} \/ {D,E,F,J,M} is non empty set
{D,E} is non empty set
{F,J,M} is non empty set
{D,E} \/ {F,J,M} is non empty set
{A,B,C} \/ ({D,E} \/ {F,J,M}) is non empty set
{E,D,F,J,M} is non empty set
{A,B,C} \/ {E,D,F,J,M} is non empty set
{A,B,C,E,D,F,J,M} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
CompF (F,G) is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
(((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
{E,F,J,M} is non empty set
{A,B,C,D} \/ {E,F,J,M} is non empty set
{E,F} is non empty set
{J,M} is non empty set
{E,F} \/ {J,M} is non empty set
{A,B,C,D} \/ ({E,F} \/ {J,M}) is non empty set
{F,E,J,M} is non empty set
{A,B,C,D} \/ {F,E,J,M} is non empty set
{A,B,C,D,F,E,J,M} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
CompF (J,G) is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
(((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
{F,J,M} is non empty set
{A,B,C,D,E} \/ {F,J,M} is non empty set
{J,F} is non empty set
{M} is non empty Element of bool (PARTITIONS Y)
{J,F} \/ {M} is non empty set
{A,B,C,D,E} \/ ({J,F} \/ {M}) is non empty set
{J,F,M} is non empty set
{A,B,C,D,E} \/ {J,F,M} is non empty set
{A,B,C,D,E,J,F,M} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
CompF (M,G) is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
{J,M} is non empty set
{A,B,C,D,E,F} \/ {J,M} is non empty set
{A,B,C,D,E,F,M,J} is non empty set
Y is set
G is set
A is set
B is set
C is set
D is set
E is set
F is set
J is Relation-like Function-like set
J . G is set
J . A is set
J . B is set
J . C is set
J . D is set
J . E is set
N is set
G .--> N is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> N is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{N}) Element of bool [:{G},{N}:]
{N} is non empty set
[:{G},{N}:] is non empty set
bool [:{G},{N}:] is non empty set
z is set
A .--> z is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> z is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{z}) Element of bool [:{A},{z}:]
{z} is non empty set
[:{A},{z}:] is non empty set
bool [:{A},{z}:] is non empty set
(G .--> N) +* (A .--> z) is Relation-like Function-like set
u is set
B .--> u is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> u is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{u}) Element of bool [:{B},{u}:]
{u} is non empty set
[:{B},{u}:] is non empty set
bool [:{B},{u}:] is non empty set
((G .--> N) +* (A .--> z)) +* (B .--> u) is Relation-like Function-like set
h is set
C .--> h is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> h is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{h}) Element of bool [:{C},{h}:]
{h} is non empty set
[:{C},{h}:] is non empty set
bool [:{C},{h}:] is non empty set
(((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h) is Relation-like Function-like set
L is set
D .--> L is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> L is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{L}) Element of bool [:{D},{L}:]
{L} is non empty set
[:{D},{L}:] is non empty set
bool [:{D},{L}:] is non empty set
((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L) is Relation-like Function-like set
GG is set
E .--> GG is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> GG is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{GG}) Element of bool [:{E},{GG}:]
{GG} is non empty set
[:{E},{GG}:] is non empty set
bool [:{E},{GG}:] is non empty set
(((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG) is Relation-like Function-like set
I is set
F .--> I is trivial Relation-like {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> I is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{I}) Element of bool [:{F},{I}:]
{I} is non empty set
[:{F},{I}:] is non empty set
bool [:{F},{I}:] is non empty set
((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I) is Relation-like Function-like set
M is set
Y .--> M is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> M is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{M}) Element of bool [:{Y},{M}:]
{M} is non empty set
[:{Y},{M}:] is non empty set
bool [:{Y},{M}:] is non empty set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) +* (Y .--> M) is Relation-like Function-like set
dom (Y .--> M) is set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) . A is set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) . E is set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) . D is set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) . C is set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) . B is set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) . G is set
G is set
A is set
B is set
C is set
D is set
E is set
F is set
Y is set
{Y,G,A,B,C,D,E,F} is non empty set
J is Relation-like Function-like set
dom J is set
N is set
G .--> N is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> N is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{N}) Element of bool [:{G},{N}:]
{N} is non empty set
[:{G},{N}:] is non empty set
bool [:{G},{N}:] is non empty set
z is set
A .--> z is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> z is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{z}) Element of bool [:{A},{z}:]
{z} is non empty set
[:{A},{z}:] is non empty set
bool [:{A},{z}:] is non empty set
(G .--> N) +* (A .--> z) is Relation-like Function-like set
u is set
B .--> u is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> u is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{u}) Element of bool [:{B},{u}:]
{u} is non empty set
[:{B},{u}:] is non empty set
bool [:{B},{u}:] is non empty set
((G .--> N) +* (A .--> z)) +* (B .--> u) is Relation-like Function-like set
h is set
C .--> h is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> h is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{h}) Element of bool [:{C},{h}:]
{h} is non empty set
[:{C},{h}:] is non empty set
bool [:{C},{h}:] is non empty set
(((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h) is Relation-like Function-like set
L is set
D .--> L is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> L is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{L}) Element of bool [:{D},{L}:]
{L} is non empty set
[:{D},{L}:] is non empty set
bool [:{D},{L}:] is non empty set
((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L) is Relation-like Function-like set
GG is set
E .--> GG is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> GG is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{GG}) Element of bool [:{E},{GG}:]
{GG} is non empty set
[:{E},{GG}:] is non empty set
bool [:{E},{GG}:] is non empty set
(((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG) is Relation-like Function-like set
I is set
F .--> I is trivial Relation-like {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> I is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{I}) Element of bool [:{F},{I}:]
{I} is non empty set
[:{F},{I}:] is non empty set
bool [:{F},{I}:] is non empty set
((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I) is Relation-like Function-like set
M is set
Y .--> M is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> M is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{M}) Element of bool [:{Y},{M}:]
{M} is non empty set
[:{Y},{M}:] is non empty set
bool [:{Y},{M}:] is non empty set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) +* (Y .--> M) is Relation-like Function-like set
dom (Y .--> M) is set
dom (((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) is set
{F,G,A,B,C,D,E} is non empty set
{G,A,B,C,D,E} is non empty set
{F} \/ {G,A,B,C,D,E} is non empty set
{G,A,B,C,D,E,F} is non empty set
dom ((((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) +* (Y .--> M)) is set
{G,A,B,C,D,E,F} \/ {Y} is non empty set
G is set
A is set
B is set
C is set
D is set
E is set
F is set
Y is set
J is Relation-like Function-like set
rng J is set
J . Y is set
J . G is set
J . A is set
J . B is set
J . C is set
J . D is set
J . E is set
J . F is set
{(J . Y),(J . G),(J . A),(J . B),(J . C),(J . D),(J . E),(J . F)} is non empty set
N is set
G .--> N is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> N is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{N}) Element of bool [:{G},{N}:]
{N} is non empty set
[:{G},{N}:] is non empty set
bool [:{G},{N}:] is non empty set
z is set
A .--> z is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> z is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{z}) Element of bool [:{A},{z}:]
{z} is non empty set
[:{A},{z}:] is non empty set
bool [:{A},{z}:] is non empty set
(G .--> N) +* (A .--> z) is Relation-like Function-like set
u is set
B .--> u is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> u is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{u}) Element of bool [:{B},{u}:]
{u} is non empty set
[:{B},{u}:] is non empty set
bool [:{B},{u}:] is non empty set
((G .--> N) +* (A .--> z)) +* (B .--> u) is Relation-like Function-like set
h is set
C .--> h is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> h is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{h}) Element of bool [:{C},{h}:]
{h} is non empty set
[:{C},{h}:] is non empty set
bool [:{C},{h}:] is non empty set
(((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h) is Relation-like Function-like set
L is set
D .--> L is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> L is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{L}) Element of bool [:{D},{L}:]
{L} is non empty set
[:{D},{L}:] is non empty set
bool [:{D},{L}:] is non empty set
((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L) is Relation-like Function-like set
GG is set
E .--> GG is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> GG is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{GG}) Element of bool [:{E},{GG}:]
{GG} is non empty set
[:{E},{GG}:] is non empty set
bool [:{E},{GG}:] is non empty set
(((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG) is Relation-like Function-like set
I is set
F .--> I is trivial Relation-like {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> I is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{I}) Element of bool [:{F},{I}:]
{I} is non empty set
[:{F},{I}:] is non empty set
bool [:{F},{I}:] is non empty set
((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I) is Relation-like Function-like set
M is set
Y .--> M is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> M is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{M}) Element of bool [:{Y},{M}:]
{M} is non empty set
[:{Y},{M}:] is non empty set
bool [:{Y},{M}:] is non empty set
(((((((G .--> N) +* (A .--> z)) +* (B .--> u)) +* (C .--> h)) +* (D .--> L)) +* (E .--> GG)) +* (F .--> I)) +* (Y .--> M) is Relation-like Function-like set
dom J is set
{Y,G,A,B,C,D,E,F} is non empty set
HH is set
FF is set
J . FF is set
HH is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
z is Element of Y
EqClass (z,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of (((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M
N is Element of Y
EqClass (N,A) is Element of A
(EqClass (z,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M))) /\ (EqClass (N,A)) is Element of bool Y
EqClass (z,B) is Element of B
B .--> (EqClass (z,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (z,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (z,B))}) Element of bool [:{B},{(EqClass (z,B))}:]
{(EqClass (z,B))} is non empty set
[:{B},{(EqClass (z,B))}:] is non empty set
bool [:{B},{(EqClass (z,B))}:] is non empty set
EqClass (z,C) is Element of C
C .--> (EqClass (z,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (z,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (z,C))}) Element of bool [:{C},{(EqClass (z,C))}:]
{(EqClass (z,C))} is non empty set
[:{C},{(EqClass (z,C))}:] is non empty set
bool [:{C},{(EqClass (z,C))}:] is non empty set
(B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,D) is Element of D
D .--> (EqClass (z,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (z,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (z,D))}) Element of bool [:{D},{(EqClass (z,D))}:]
{(EqClass (z,D))} is non empty set
[:{D},{(EqClass (z,D))}:] is non empty set
bool [:{D},{(EqClass (z,D))}:] is non empty set
((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,E) is Element of E
E .--> (EqClass (z,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (z,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (z,E))}) Element of bool [:{E},{(EqClass (z,E))}:]
{(EqClass (z,E))} is non empty set
[:{E},{(EqClass (z,E))}:] is non empty set
bool [:{E},{(EqClass (z,E))}:] is non empty set
(((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,F) is Element of F
F .--> (EqClass (z,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (z,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (z,F))}) Element of bool [:{F},{(EqClass (z,F))}:]
{(EqClass (z,F))} is non empty set
[:{F},{(EqClass (z,F))}:] is non empty set
bool [:{F},{(EqClass (z,F))}:] is non empty set
((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,J) is Element of J
J .--> (EqClass (z,J)) is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined J -valued Function-like one-to-one set
{J} is non empty set
{J} --> (EqClass (z,J)) is non empty Relation-like {J} -defined J -valued Function-like constant V17({J}) V21({J},{(EqClass (z,J))}) Element of bool [:{J},{(EqClass (z,J))}:]
{(EqClass (z,J))} is non empty set
[:{J},{(EqClass (z,J))}:] is non empty set
bool [:{J},{(EqClass (z,J))}:] is non empty set
(((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,M) is Element of M
M .--> (EqClass (z,M)) is trivial Relation-like {M} -defined bool (bool Y) -defined {M} -defined M -valued Function-like one-to-one set
{M} is non empty set
{M} --> (EqClass (z,M)) is non empty Relation-like {M} -defined M -valued Function-like constant V17({M}) V21({M},{(EqClass (z,M))}) Element of bool [:{M},{(EqClass (z,M))}:]
{(EqClass (z,M))} is non empty set
[:{M},{(EqClass (z,M))}:] is non empty set
bool [:{M},{(EqClass (z,M))}:] is non empty set
((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M))) is Relation-like bool (bool Y) -defined Function-like set
A .--> (EqClass (N,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (N,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (N,A))}) Element of bool [:{A},{(EqClass (N,A))}:]
{(EqClass (N,A))} is non empty set
[:{A},{(EqClass (N,A))}:] is non empty set
bool [:{A},{(EqClass (N,A))}:] is non empty set
(((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A))) is Relation-like bool (bool Y) -defined Function-like set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . B is set
h is set
EqClass (z,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)) is Element of ((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J
(EqClass (z,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
(EqClass (z,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (z,J)) is Element of bool Y
((EqClass (z,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (z,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (z,F)) is Element of bool Y
((EqClass (z,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
(((EqClass (z,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E)) is Element of bool Y
((EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E))) /\ (EqClass (z,F)) is Element of bool Y
(((EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
((((EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,(B '/\' C)) is Element of B '/\' C
(EqClass (z,(B '/\' C))) /\ (EqClass (z,D)) is Element of bool Y
((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E)) is Element of bool Y
(((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F)) is Element of bool Y
((((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
(((((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
L is set
h /\ L is set
(EqClass (z,B)) /\ (EqClass (z,C)) is Element of bool Y
((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D)) is Element of bool Y
(((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E)) is Element of bool Y
((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F)) is Element of bool Y
(((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
((((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
(((((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M))) /\ (EqClass (N,A)) is Element of bool Y
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . A is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . C is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . M is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . J is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . F is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . E is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . D is set
rng ((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) is set
{(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . A),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . B),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . C),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . D),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . E),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . F),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . J),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . M)} is non empty set
GG is set
dom ((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) is set
GG is Element of bool (bool Y)
Intersect GG is Element of bool Y
meet (rng ((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A))))) is set
I is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . I is set
I is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M} is non empty set
C '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((C '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((C '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
N is Element of Y
EqClass (N,(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of ((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M
z is Element of Y
EqClass (z,(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of ((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M
EqClass (z,(CompF (A,G))) is Element of CompF (A,G)
EqClass (N,(CompF (B,G))) is Element of CompF (B,G)
EqClass (z,B) is Element of B
B .--> (EqClass (z,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (z,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (z,B))}) Element of bool [:{B},{(EqClass (z,B))}:]
{(EqClass (z,B))} is non empty set
[:{B},{(EqClass (z,B))}:] is non empty set
bool [:{B},{(EqClass (z,B))}:] is non empty set
EqClass (z,C) is Element of C
C .--> (EqClass (z,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (z,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (z,C))}) Element of bool [:{C},{(EqClass (z,C))}:]
{(EqClass (z,C))} is non empty set
[:{C},{(EqClass (z,C))}:] is non empty set
bool [:{C},{(EqClass (z,C))}:] is non empty set
(B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,D) is Element of D
D .--> (EqClass (z,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (z,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (z,D))}) Element of bool [:{D},{(EqClass (z,D))}:]
{(EqClass (z,D))} is non empty set
[:{D},{(EqClass (z,D))}:] is non empty set
bool [:{D},{(EqClass (z,D))}:] is non empty set
((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,E) is Element of E
E .--> (EqClass (z,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (z,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (z,E))}) Element of bool [:{E},{(EqClass (z,E))}:]
{(EqClass (z,E))} is non empty set
[:{E},{(EqClass (z,E))}:] is non empty set
bool [:{E},{(EqClass (z,E))}:] is non empty set
(((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,F) is Element of F
F .--> (EqClass (z,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (z,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (z,F))}) Element of bool [:{F},{(EqClass (z,F))}:]
{(EqClass (z,F))} is non empty set
[:{F},{(EqClass (z,F))}:] is non empty set
bool [:{F},{(EqClass (z,F))}:] is non empty set
((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,J) is Element of J
J .--> (EqClass (z,J)) is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined J -valued Function-like one-to-one set
{J} is non empty set
{J} --> (EqClass (z,J)) is non empty Relation-like {J} -defined J -valued Function-like constant V17({J}) V21({J},{(EqClass (z,J))}) Element of bool [:{J},{(EqClass (z,J))}:]
{(EqClass (z,J))} is non empty set
[:{J},{(EqClass (z,J))}:] is non empty set
bool [:{J},{(EqClass (z,J))}:] is non empty set
(((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,M) is Element of M
M .--> (EqClass (z,M)) is trivial Relation-like {M} -defined bool (bool Y) -defined {M} -defined M -valued Function-like one-to-one set
{M} is non empty set
{M} --> (EqClass (z,M)) is non empty Relation-like {M} -defined M -valued Function-like constant V17({M}) V21({M},{(EqClass (z,M))}) Element of bool [:{M},{(EqClass (z,M))}:]
{(EqClass (z,M))} is non empty set
[:{M},{(EqClass (z,M))}:] is non empty set
bool [:{M},{(EqClass (z,M))}:] is non empty set
((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (N,A) is Element of A
A .--> (EqClass (N,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (N,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (N,A))}) Element of bool [:{A},{(EqClass (N,A))}:]
{(EqClass (N,A))} is non empty set
[:{A},{(EqClass (N,A))}:] is non empty set
bool [:{A},{(EqClass (N,A))}:] is non empty set
(((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A))) is Relation-like bool (bool Y) -defined Function-like set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . B is set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
EqClass (z,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of (((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M
EqClass (z,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)) is Element of ((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J
(EqClass (z,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
(EqClass (z,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (z,J)) is Element of bool Y
((EqClass (z,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (z,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (z,F)) is Element of bool Y
((EqClass (z,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
(((EqClass (z,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E)) is Element of bool Y
((EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E))) /\ (EqClass (z,F)) is Element of bool Y
(((EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
((((EqClass (z,((B '/\' C) '/\' D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
EqClass (z,(B '/\' C)) is Element of B '/\' C
(EqClass (z,(B '/\' C))) /\ (EqClass (z,D)) is Element of bool Y
((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E)) is Element of bool Y
(((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F)) is Element of bool Y
((((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
(((((EqClass (z,(B '/\' C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
(EqClass (z,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M))) /\ (EqClass (N,A)) is Element of bool Y
(EqClass (z,B)) /\ (EqClass (z,C)) is Element of bool Y
((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D)) is Element of bool Y
(((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E)) is Element of bool Y
((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F)) is Element of bool Y
(((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J)) is Element of bool Y
((((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M)) is Element of bool Y
(((((((EqClass (z,B)) /\ (EqClass (z,C))) /\ (EqClass (z,D))) /\ (EqClass (z,E))) /\ (EqClass (z,F))) /\ (EqClass (z,J))) /\ (EqClass (z,M))) /\ (EqClass (N,A)) is Element of bool Y
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . A is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . C is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . M is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . J is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . F is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . E is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . D is set
rng ((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) is set
{(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . A),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . B),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . C),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . D),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . E),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . F),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . J),(((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . M)} is non empty set
I is set
dom ((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) is set
I is Element of bool (bool Y)
Intersect I is Element of bool Y
meet (rng ((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A))))) is set
HH is set
((((((((B .--> (EqClass (z,B))) +* (C .--> (EqClass (z,C)))) +* (D .--> (EqClass (z,D)))) +* (E .--> (EqClass (z,E)))) +* (F .--> (EqClass (z,F)))) +* (J .--> (EqClass (z,J)))) +* (M .--> (EqClass (z,M)))) +* (A .--> (EqClass (N,A)))) . HH is set
HH is set
FF is set
m is Element of Y
EqClass (m,(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of ((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((B '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
EqClass (z,(((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of ((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M
B '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(B '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
EqClass (z,((((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M)) is Element of (((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M
B '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
(B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J is non empty with_non-empty_elements a_partition of Y
((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
EqClass (z,(((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M)) is Element of ((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M
B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J) is non empty with_non-empty_elements a_partition of Y
(B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M is non empty with_non-empty_elements a_partition of Y
EqClass (z,((B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M)) is Element of (B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M
B '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) is non empty with_non-empty_elements a_partition of Y
EqClass (z,(B '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M))) is Element of B '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)
p is set
p is set
(EqClass (N,A)) /\ p is Element of bool Y
A '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) is non empty with_non-empty_elements a_partition of Y
A '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J) is non empty with_non-empty_elements a_partition of Y
(A '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M is non empty with_non-empty_elements a_partition of Y
A '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
(A '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J is non empty with_non-empty_elements a_partition of Y
((A '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
A '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(A '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
((A '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((A '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
A '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(A '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((A '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((A '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((A '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
INTERSECTION (A,(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is set
(INTERSECTION (A,(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M))) \ {{}} is Element of bool (INTERSECTION (A,(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)))
bool (INTERSECTION (A,(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M))) is non empty set
Y is set
G is set
A is set
B is set
{Y,G,A,B} is non empty set
C is set
D is set
E is set
F is set
J is set
{Y,G,A,B,C,D,E,F,J} is non empty set
{C,D,E,F,J} is non empty set
{Y,G,A,B} \/ {C,D,E,F,J} is non empty set
M is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
{A} is non empty Element of bool (PARTITIONS Y)
{D,E} is non empty set
{D,E} \ {A} is Element of bool {D,E}
bool {D,E} is non empty set
G \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E,F,J,M,N} is non empty set
{A} \/ {B,C,D,E,F,J,M,N} is non empty set
({A} \/ {B,C,D,E,F,J,M,N}) \ {A} is Element of bool ({A} \/ {B,C,D,E,F,J,M,N})
bool ({A} \/ {B,C,D,E,F,J,M,N}) is non empty set
{A} \ {A} is Element of bool (PARTITIONS Y)
{B,C,D,E,F,J,M,N} \ {A} is Element of bool {B,C,D,E,F,J,M,N}
bool {B,C,D,E,F,J,M,N} is non empty set
({A} \ {A}) \/ ({B,C,D,E,F,J,M,N} \ {A}) is set
{B} is non empty Element of bool (PARTITIONS Y)
{C,D,E,F,J,M,N} is non empty set
{B} \/ {C,D,E,F,J,M,N} is non empty set
({B} \/ {C,D,E,F,J,M,N}) \ {A} is Element of bool ({B} \/ {C,D,E,F,J,M,N})
bool ({B} \/ {C,D,E,F,J,M,N}) is non empty set
{B} \ {A} is Element of bool (PARTITIONS Y)
{C,D,E,F,J,M,N} \ {A} is Element of bool {C,D,E,F,J,M,N}
bool {C,D,E,F,J,M,N} is non empty set
({B} \ {A}) \/ ({C,D,E,F,J,M,N} \ {A}) is set
{B} \/ ({C,D,E,F,J,M,N} \ {A}) is non empty set
{C} is non empty Element of bool (PARTITIONS Y)
{D,E,F,J,M,N} is non empty set
{C} \/ {D,E,F,J,M,N} is non empty set
({C} \/ {D,E,F,J,M,N}) \ {A} is Element of bool ({C} \/ {D,E,F,J,M,N})
bool ({C} \/ {D,E,F,J,M,N}) is non empty set
{B} \/ (({C} \/ {D,E,F,J,M,N}) \ {A}) is non empty set
{C} \ {A} is Element of bool (PARTITIONS Y)
{D,E,F,J,M,N} \ {A} is Element of bool {D,E,F,J,M,N}
bool {D,E,F,J,M,N} is non empty set
({C} \ {A}) \/ ({D,E,F,J,M,N} \ {A}) is set
{B} \/ (({C} \ {A}) \/ ({D,E,F,J,M,N} \ {A})) is non empty set
{F,J,M,N} is non empty set
{D,E} \/ {F,J,M,N} is non empty set
({D,E} \/ {F,J,M,N}) \ {A} is Element of bool ({D,E} \/ {F,J,M,N})
bool ({D,E} \/ {F,J,M,N}) is non empty set
({C} \ {A}) \/ (({D,E} \/ {F,J,M,N}) \ {A}) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \/ {F,J,M,N}) \ {A})) is non empty set
{F,J,M,N} \ {A} is Element of bool {F,J,M,N}
bool {F,J,M,N} is non empty set
({D,E} \ {A}) \/ ({F,J,M,N} \ {A}) is set
({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F,J,M,N} \ {A})) is set
{B} \/ (({C} \ {A}) \/ (({D,E} \ {A}) \/ ({F,J,M,N} \ {A}))) is non empty set
{F,J} is non empty set
{M,N} is non empty set
{F,J} \/ {M,N} is non empty set
({F,J} \/ {M,N}) \ {A} is Element of bool ({F,J} \/ {M,N})
bool ({F,J} \/ {M,N}) is non empty set
{D,E} \/ (({F,J} \/ {M,N}) \ {A}) is non empty set
({C} \ {A}) \/ ({D,E} \/ (({F,J} \/ {M,N}) \ {A})) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ (({F,J} \/ {M,N}) \ {A}))) is non empty set
{F,J} \ {A} is Element of bool {F,J}
bool {F,J} is non empty set
{M,N} \ {A} is Element of bool {M,N}
bool {M,N} is non empty set
({F,J} \ {A}) \/ ({M,N} \ {A}) is set
{D,E} \/ (({F,J} \ {A}) \/ ({M,N} \ {A})) is non empty set
({C} \ {A}) \/ ({D,E} \/ (({F,J} \ {A}) \/ ({M,N} \ {A}))) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ (({F,J} \ {A}) \/ ({M,N} \ {A})))) is non empty set
{F,J} \/ ({M,N} \ {A}) is non empty set
{D,E} \/ ({F,J} \/ ({M,N} \ {A})) is non empty set
({C} \ {A}) \/ ({D,E} \/ ({F,J} \/ ({M,N} \ {A}))) is non empty set
{B} \/ (({C} \ {A}) \/ ({D,E} \/ ({F,J} \/ ({M,N} \ {A})))) is non empty set
{C} \/ ({D,E} \/ ({F,J} \/ ({M,N} \ {A}))) is non empty set
{B} \/ ({C} \/ ({D,E} \/ ({F,J} \/ ({M,N} \ {A})))) is non empty set
{D,E} \/ ({F,J} \/ {M,N}) is non empty set
{C} \/ ({D,E} \/ ({F,J} \/ {M,N})) is non empty set
{B} \/ ({C} \/ ({D,E} \/ ({F,J} \/ {M,N}))) is non empty set
{C} \/ ({D,E} \/ {F,J,M,N}) is non empty set
{B} \/ ({C} \/ ({D,E} \/ {F,J,M,N})) is non empty set
{B} \/ ({C} \/ {D,E,F,J,M,N}) is non empty set
{} \/ {B,C,D,E,F,J,M,N} is non empty set
'/\' (G \ {A}) is non empty with_non-empty_elements a_partition of Y
z is set
u is Relation-like Function-like set
dom u is set
rng u is set
h is Element of bool (bool Y)
Intersect h is Element of bool Y
u . C is set
u . B is set
(u . B) /\ (u . C) is set
u . D is set
((u . B) /\ (u . C)) /\ (u . D) is set
u . E is set
u . N is set
INTERSECTION (B,C) is set
meet (rng u) is set
u . F is set
u . M is set
u . J is set
(((u . B) /\ (u . C)) /\ (u . D)) /\ (u . E) is set
((((u . B) /\ (u . C)) /\ (u . D)) /\ (u . E)) /\ (u . F) is set
(((((u . B) /\ (u . C)) /\ (u . D)) /\ (u . E)) /\ (u . F)) /\ (u . J) is set
((((((u . B) /\ (u . C)) /\ (u . D)) /\ (u . E)) /\ (u . F)) /\ (u . J)) /\ (u . M) is set
(((((((u . B) /\ (u . C)) /\ (u . D)) /\ (u . E)) /\ (u . F)) /\ (u . J)) /\ (u . M)) /\ (u . N) is set
I is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
{(u . B),(u . C),(u . D),(u . E),(u . F),(u . J),(u . M),(u . N)} is non empty set
p is set
p is set
u . p is set
p is set
p is set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J) is set
(INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) \ {{}} is Element of bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J))
bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) is non empty set
INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M) is set
(INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) \ {{}} is Element of bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M))
bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) is non empty set
INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N) is set
(INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N)) \ {{}} is Element of bool (INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N))
bool (INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N)) is non empty set
z is set
INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N) is set
(INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N)) \ {{}} is Element of bool (INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N))
bool (INTERSECTION (((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M),N)) is non empty set
u is set
h is set
u /\ h is set
INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M) is set
(INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) \ {{}} is Element of bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M))
bool (INTERSECTION ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J),M)) is non empty set
L is set
GG is set
L /\ GG is set
INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J) is set
(INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) \ {{}} is Element of bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J))
bool (INTERSECTION (((((B '/\' C) '/\' D) '/\' E) '/\' F),J)) is non empty set
I is set
HH is set
I /\ HH is set
INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F) is set
(INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) \ {{}} is Element of bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F))
bool (INTERSECTION ((((B '/\' C) '/\' D) '/\' E),F)) is non empty set
FF is set
m is set
FF /\ m is set
INTERSECTION (((B '/\' C) '/\' D),E) is set
(INTERSECTION (((B '/\' C) '/\' D),E)) \ {{}} is Element of bool (INTERSECTION (((B '/\' C) '/\' D),E))
bool (INTERSECTION (((B '/\' C) '/\' D),E)) is non empty set
p is set
p is set
p /\ p is set
INTERSECTION ((B '/\' C),D) is set
(INTERSECTION ((B '/\' C),D)) \ {{}} is Element of bool (INTERSECTION ((B '/\' C),D))
bool (INTERSECTION ((B '/\' C),D)) is non empty set
K is set
d is set
K /\ d is set
INTERSECTION (B,C) is set
(INTERSECTION (B,C)) \ {{}} is Element of bool (INTERSECTION (B,C))
bool (INTERSECTION (B,C)) is non empty set
b is set
c is set
b /\ c is set
B .--> b is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> b is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{b}) Element of bool [:{B},{b}:]
{b} is non empty set
[:{B},{b}:] is non empty set
bool [:{B},{b}:] is non empty set
C .--> c is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> c is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{c}) Element of bool [:{C},{c}:]
{c} is non empty set
[:{C},{c}:] is non empty set
bool [:{C},{c}:] is non empty set
(B .--> b) +* (C .--> c) is Relation-like bool (bool Y) -defined Function-like set
D .--> d is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> d is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{d}) Element of bool [:{D},{d}:]
{d} is non empty set
[:{D},{d}:] is non empty set
bool [:{D},{d}:] is non empty set
((B .--> b) +* (C .--> c)) +* (D .--> d) is Relation-like bool (bool Y) -defined Function-like set
E .--> p is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> p is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{p}) Element of bool [:{E},{p}:]
{p} is non empty set
[:{E},{p}:] is non empty set
bool [:{E},{p}:] is non empty set
(((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p) is Relation-like bool (bool Y) -defined Function-like set
F .--> m is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> m is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{m}) Element of bool [:{F},{m}:]
{m} is non empty set
[:{F},{m}:] is non empty set
bool [:{F},{m}:] is non empty set
((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m) is Relation-like bool (bool Y) -defined Function-like set
J .--> HH is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined Function-like one-to-one set
{J} is non empty set
{J} --> HH is non empty Relation-like {J} -defined Function-like constant V17({J}) V21({J},{HH}) Element of bool [:{J},{HH}:]
{HH} is non empty set
[:{J},{HH}:] is non empty set
bool [:{J},{HH}:] is non empty set
(((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH) is Relation-like bool (bool Y) -defined Function-like set
M .--> GG is trivial Relation-like {M} -defined bool (bool Y) -defined {M} -defined Function-like one-to-one set
{M} is non empty set
{M} --> GG is non empty Relation-like {M} -defined Function-like constant V17({M}) V21({M},{GG}) Element of bool [:{M},{GG}:]
{GG} is non empty set
[:{M},{GG}:] is non empty set
bool [:{M},{GG}:] is non empty set
((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG) is Relation-like bool (bool Y) -defined Function-like set
N .--> h is trivial Relation-like {N} -defined bool (bool Y) -defined {N} -defined Function-like one-to-one set
{N} is non empty set
{N} --> h is non empty Relation-like {N} -defined Function-like constant V17({N}) V21({N},{h}) Element of bool [:{N},{h}:]
{h} is non empty set
[:{N},{h}:] is non empty set
bool [:{N},{h}:] is non empty set
(((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h) is Relation-like bool (bool Y) -defined Function-like set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . N is set
dom ((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) is set
{N,B,C,D,E,F,J,M} is non empty set
{N} is non empty Element of bool (PARTITIONS Y)
{B,C,D,E,F,J,M} is non empty set
{N} \/ {B,C,D,E,F,J,M} is non empty set
FF is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . FF is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . D is set
rng ((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . B is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . C is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . E is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . F is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . J is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . M is set
{(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . B),(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . C),(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . D),(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . E),(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . F),(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . J),(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . M),(((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . N)} is non empty set
FF is set
h is set
((((((((B .--> b) +* (C .--> c)) +* (D .--> d)) +* (E .--> p)) +* (F .--> m)) +* (J .--> HH)) +* (M .--> GG)) +* (N .--> h)) . h is set
FF is set
h is set
FF is Element of bool (bool Y)
Intersect FF is Element of bool Y
t is set
y is set
h is Relation-like Function-like set
h . D is set
(b /\ c) /\ p is set
d /\ ((b /\ c) /\ p) is set
(d /\ ((b /\ c) /\ p)) /\ m is set
((d /\ ((b /\ c) /\ p)) /\ m) /\ HH is set
(((d /\ ((b /\ c) /\ p)) /\ m) /\ HH) /\ GG is set
((((d /\ ((b /\ c) /\ p)) /\ m) /\ HH) /\ GG) /\ h is set
((b /\ c) /\ p) /\ m is set
d /\ (((b /\ c) /\ p) /\ m) is set
(d /\ (((b /\ c) /\ p) /\ m)) /\ HH is set
((d /\ (((b /\ c) /\ p) /\ m)) /\ HH) /\ GG is set
(((d /\ (((b /\ c) /\ p) /\ m)) /\ HH) /\ GG) /\ h is set
(((b /\ c) /\ p) /\ m) /\ HH is set
d /\ ((((b /\ c) /\ p) /\ m) /\ HH) is set
(d /\ ((((b /\ c) /\ p) /\ m) /\ HH)) /\ GG is set
((d /\ ((((b /\ c) /\ p) /\ m) /\ HH)) /\ GG) /\ h is set
((((b /\ c) /\ p) /\ m) /\ HH) /\ GG is set
d /\ (((((b /\ c) /\ p) /\ m) /\ HH) /\ GG) is set
(d /\ (((((b /\ c) /\ p) /\ m) /\ HH) /\ GG)) /\ h is set
(((((b /\ c) /\ p) /\ m) /\ HH) /\ GG) /\ h is set
d /\ ((((((b /\ c) /\ p) /\ m) /\ HH) /\ GG) /\ h) is set
h is Relation-like Function-like set
h . B is set
d /\ b is set
c /\ (d /\ b) is set
(c /\ (d /\ b)) /\ p is set
((c /\ (d /\ b)) /\ p) /\ m is set
(((c /\ (d /\ b)) /\ p) /\ m) /\ HH is set
((((c /\ (d /\ b)) /\ p) /\ m) /\ HH) /\ GG is set
(((((c /\ (d /\ b)) /\ p) /\ m) /\ HH) /\ GG) /\ h is set
(d /\ b) /\ p is set
c /\ ((d /\ b) /\ p) is set
(c /\ ((d /\ b) /\ p)) /\ m is set
((c /\ ((d /\ b) /\ p)) /\ m) /\ HH is set
(((c /\ ((d /\ b) /\ p)) /\ m) /\ HH) /\ GG is set
((((c /\ ((d /\ b) /\ p)) /\ m) /\ HH) /\ GG) /\ h is set
d /\ p is set
(d /\ p) /\ b is set
c /\ ((d /\ p) /\ b) is set
(c /\ ((d /\ p) /\ b)) /\ m is set
((c /\ ((d /\ p) /\ b)) /\ m) /\ HH is set
(((c /\ ((d /\ p) /\ b)) /\ m) /\ HH) /\ GG is set
((((c /\ ((d /\ p) /\ b)) /\ m) /\ HH) /\ GG) /\ h is set
((d /\ p) /\ b) /\ m is set
c /\ (((d /\ p) /\ b) /\ m) is set
(c /\ (((d /\ p) /\ b) /\ m)) /\ HH is set
((c /\ (((d /\ p) /\ b) /\ m)) /\ HH) /\ GG is set
(((c /\ (((d /\ p) /\ b) /\ m)) /\ HH) /\ GG) /\ h is set
(((d /\ p) /\ b) /\ m) /\ HH is set
c /\ ((((d /\ p) /\ b) /\ m) /\ HH) is set
(c /\ ((((d /\ p) /\ b) /\ m) /\ HH)) /\ GG is set
((c /\ ((((d /\ p) /\ b) /\ m) /\ HH)) /\ GG) /\ h is set
m /\ b is set
(d /\ p) /\ (m /\ b) is set
((d /\ p) /\ (m /\ b)) /\ HH is set
c /\ (((d /\ p) /\ (m /\ b)) /\ HH) is set
(c /\ (((d /\ p) /\ (m /\ b)) /\ HH)) /\ GG is set
((c /\ (((d /\ p) /\ (m /\ b)) /\ HH)) /\ GG) /\ h is set
(m /\ b) /\ HH is set
(d /\ p) /\ ((m /\ b) /\ HH) is set
c /\ ((d /\ p) /\ ((m /\ b) /\ HH)) is set
(c /\ ((d /\ p) /\ ((m /\ b) /\ HH))) /\ GG is set
((c /\ ((d /\ p) /\ ((m /\ b) /\ HH))) /\ GG) /\ h is set
HH /\ b is set
m /\ (HH /\ b) is set
(d /\ p) /\ (m /\ (HH /\ b)) is set
c /\ ((d /\ p) /\ (m /\ (HH /\ b))) is set
(c /\ ((d /\ p) /\ (m /\ (HH /\ b)))) /\ GG is set
((c /\ ((d /\ p) /\ (m /\ (HH /\ b)))) /\ GG) /\ h is set
c /\ (d /\ p) is set
(c /\ (d /\ p)) /\ (m /\ (HH /\ b)) is set
((c /\ (d /\ p)) /\ (m /\ (HH /\ b))) /\ GG is set
(((c /\ (d /\ p)) /\ (m /\ (HH /\ b))) /\ GG) /\ h is set
(c /\ (d /\ p)) /\ m is set
((c /\ (d /\ p)) /\ m) /\ (HH /\ b) is set
(((c /\ (d /\ p)) /\ m) /\ (HH /\ b)) /\ GG is set
((((c /\ (d /\ p)) /\ m) /\ (HH /\ b)) /\ GG) /\ h is set
((c /\ (d /\ p)) /\ m) /\ HH is set
(((c /\ (d /\ p)) /\ m) /\ HH) /\ b is set
((((c /\ (d /\ p)) /\ m) /\ HH) /\ b) /\ GG is set
(((((c /\ (d /\ p)) /\ m) /\ HH) /\ b) /\ GG) /\ h is set
GG /\ b is set
(((c /\ (d /\ p)) /\ m) /\ HH) /\ (GG /\ b) is set
((((c /\ (d /\ p)) /\ m) /\ HH) /\ (GG /\ b)) /\ h is set
(GG /\ b) /\ h is set
(((c /\ (d /\ p)) /\ m) /\ HH) /\ ((GG /\ b) /\ h) is set
b /\ h is set
GG /\ (b /\ h) is set
(((c /\ (d /\ p)) /\ m) /\ HH) /\ (GG /\ (b /\ h)) is set
(((c /\ (d /\ p)) /\ m) /\ HH) /\ GG is set
h /\ b is set
((((c /\ (d /\ p)) /\ m) /\ HH) /\ GG) /\ (h /\ b) is set
((((c /\ (d /\ p)) /\ m) /\ HH) /\ GG) /\ h is set
(((((c /\ (d /\ p)) /\ m) /\ HH) /\ GG) /\ h) /\ b is set
h is Relation-like Function-like set
h . C is set
d /\ b is set
c /\ (d /\ b) is set
(c /\ (d /\ b)) /\ p is set
((c /\ (d /\ b)) /\ p) /\ m is set
(((c /\ (d /\ b)) /\ p) /\ m) /\ HH is set
((((c /\ (d /\ b)) /\ p) /\ m) /\ HH) /\ GG is set
(((((c /\ (d /\ b)) /\ p) /\ m) /\ HH) /\ GG) /\ h is set
(d /\ b) /\ p is set
c /\ ((d /\ b) /\ p) is set
(c /\ ((d /\ b) /\ p)) /\ m is set
((c /\ ((d /\ b) /\ p)) /\ m) /\ HH is set
(((c /\ ((d /\ b) /\ p)) /\ m) /\ HH) /\ GG is set
((((c /\ ((d /\ b) /\ p)) /\ m) /\ HH) /\ GG) /\ h is set
d /\ p is set
(d /\ p) /\ b is set
c /\ ((d /\ p) /\ b) is set
(c /\ ((d /\ p) /\ b)) /\ m is set
((c /\ ((d /\ p) /\ b)) /\ m) /\ HH is set
(((c /\ ((d /\ p) /\ b)) /\ m) /\ HH) /\ GG is set
((((c /\ ((d /\ p) /\ b)) /\ m) /\ HH) /\ GG) /\ h is set
((d /\ p) /\ b) /\ m is set
c /\ (((d /\ p) /\ b) /\ m) is set
(c /\ (((d /\ p) /\ b) /\ m)) /\ HH is set
((c /\ (((d /\ p) /\ b) /\ m)) /\ HH) /\ GG is set
(((c /\ (((d /\ p) /\ b) /\ m)) /\ HH) /\ GG) /\ h is set
(((d /\ p) /\ b) /\ m) /\ HH is set
c /\ ((((d /\ p) /\ b) /\ m) /\ HH) is set
(c /\ ((((d /\ p) /\ b) /\ m) /\ HH)) /\ GG is set
((c /\ ((((d /\ p) /\ b) /\ m) /\ HH)) /\ GG) /\ h is set
((((d /\ p) /\ b) /\ m) /\ HH) /\ GG is set
c /\ (((((d /\ p) /\ b) /\ m) /\ HH) /\ GG) is set
(c /\ (((((d /\ p) /\ b) /\ m) /\ HH) /\ GG)) /\ h is set
(((((d /\ p) /\ b) /\ m) /\ HH) /\ GG) /\ h is set
c /\ ((((((d /\ p) /\ b) /\ m) /\ HH) /\ GG) /\ h) is set
h is Relation-like Function-like set
h . E is set
(b /\ c) /\ d is set
m /\ p is set
((b /\ c) /\ d) /\ (m /\ p) is set
(((b /\ c) /\ d) /\ (m /\ p)) /\ HH is set
((((b /\ c) /\ d) /\ (m /\ p)) /\ HH) /\ GG is set
(((((b /\ c) /\ d) /\ (m /\ p)) /\ HH) /\ GG) /\ h is set
(m /\ p) /\ HH is set
((b /\ c) /\ d) /\ ((m /\ p) /\ HH) is set
(((b /\ c) /\ d) /\ ((m /\ p) /\ HH)) /\ GG is set
((((b /\ c) /\ d) /\ ((m /\ p) /\ HH)) /\ GG) /\ h is set
m /\ HH is set
(m /\ HH) /\ p is set
((b /\ c) /\ d) /\ ((m /\ HH) /\ p) is set
(((b /\ c) /\ d) /\ ((m /\ HH) /\ p)) /\ GG is set
((((b /\ c) /\ d) /\ ((m /\ HH) /\ p)) /\ GG) /\ h is set
((b /\ c) /\ d) /\ (m /\ HH) is set
(((b /\ c) /\ d) /\ (m /\ HH)) /\ p is set
((((b /\ c) /\ d) /\ (m /\ HH)) /\ p) /\ GG is set
(((((b /\ c) /\ d) /\ (m /\ HH)) /\ p) /\ GG) /\ h is set
p /\ GG is set
(((b /\ c) /\ d) /\ (m /\ HH)) /\ (p /\ GG) is set
((((b /\ c) /\ d) /\ (m /\ HH)) /\ (p /\ GG)) /\ h is set
GG /\ p is set
(GG /\ p) /\ h is set
(((b /\ c) /\ d) /\ (m /\ HH)) /\ ((GG /\ p) /\ h) is set
h /\ p is set
GG /\ (h /\ p) is set
(((b /\ c) /\ d) /\ (m /\ HH)) /\ (GG /\ (h /\ p)) is set
(((b /\ c) /\ d) /\ (m /\ HH)) /\ GG is set
((((b /\ c) /\ d) /\ (m /\ HH)) /\ GG) /\ (h /\ p) is set
((((b /\ c) /\ d) /\ (m /\ HH)) /\ GG) /\ h is set
(((((b /\ c) /\ d) /\ (m /\ HH)) /\ GG) /\ h) /\ p is set
h is Relation-like Function-like set
h . F is set
(b /\ c) /\ d is set
((b /\ c) /\ d) /\ p is set
(((b /\ c) /\ d) /\ p) /\ HH is set
((((b /\ c) /\ d) /\ p) /\ HH) /\ m is set
(((((b /\ c) /\ d) /\ p) /\ HH) /\ m) /\ GG is set
((((((b /\ c) /\ d) /\ p) /\ HH) /\ m) /\ GG) /\ h is set
((((b /\ c) /\ d) /\ p) /\ HH) /\ GG is set
(((((b /\ c) /\ d) /\ p) /\ HH) /\ GG) /\ m is set
((((((b /\ c) /\ d) /\ p) /\ HH) /\ GG) /\ m) /\ h is set
(((((b /\ c) /\ d) /\ p) /\ HH) /\ GG) /\ h is set
((((((b /\ c) /\ d) /\ p) /\ HH) /\ GG) /\ h) /\ m is set
h is Relation-like Function-like set
h . J is set
(b /\ c) /\ d is set
((b /\ c) /\ d) /\ p is set
(((b /\ c) /\ d) /\ p) /\ m is set
((((b /\ c) /\ d) /\ p) /\ m) /\ GG is set
(((((b /\ c) /\ d) /\ p) /\ m) /\ GG) /\ HH is set
((((((b /\ c) /\ d) /\ p) /\ m) /\ GG) /\ HH) /\ h is set
(((((b /\ c) /\ d) /\ p) /\ m) /\ GG) /\ h is set
((((((b /\ c) /\ d) /\ p) /\ m) /\ GG) /\ h) /\ HH is set
h is Relation-like Function-like set
h . M is set
(b /\ c) /\ d is set
((b /\ c) /\ d) /\ p is set
(((b /\ c) /\ d) /\ p) /\ m is set
((((b /\ c) /\ d) /\ p) /\ m) /\ HH is set
(((((b /\ c) /\ d) /\ p) /\ m) /\ HH) /\ h is set
((((((b /\ c) /\ d) /\ p) /\ m) /\ HH) /\ h) /\ GG is set
h is Relation-like Function-like set
h . N is set
h is Relation-like Function-like set
h . D is set
h . B is set
h . C is set
h . E is set
h . F is set
h . J is set
h . M is set
h . N is set
h is Relation-like Function-like set
h . D is set
h . B is set
h . C is set
h . E is set
h . F is set
h . J is set
h . M is set
h . N is set
meet FF is Element of bool Y
h is Relation-like Function-like set
rng h is set
meet (rng h) is set
t is set
h . C is set
h . B is set
h . D is set
(b /\ c) /\ d is set
h . E is set
((b /\ c) /\ d) /\ p is set
h . F is set
(((b /\ c) /\ d) /\ p) /\ m is set
h . J is set
((((b /\ c) /\ d) /\ p) /\ m) /\ HH is set
h . M is set
(((((b /\ c) /\ d) /\ p) /\ m) /\ HH) /\ GG is set
h . N is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E,F,J,M,N} is non empty set
{A,B} \/ {C,D,E,F,J,M,N} is non empty set
{B,A,C,D,E,F,J,M,N} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (C,G) is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' D is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((A '/\' B) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F,J,M,N} is non empty set
{A,B,C} \/ {D,E,F,J,M,N} is non empty set
{A} is non empty Element of bool (PARTITIONS Y)
{B,C} is non empty set
{A} \/ {B,C} is non empty set
({A} \/ {B,C}) \/ {D,E,F,J,M,N} is non empty set
{A,C,B} is non empty set
{A,C,B} \/ {D,E,F,J,M,N} is non empty set
{A,C,B,D,E,F,J,M,N} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (D,G) is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' E is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' C) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((A '/\' B) '/\' C) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
{A,B} is non empty set
{C,D,E,F,J,M,N} is non empty set
{A,B} \/ {C,D,E,F,J,M,N} is non empty set
{C,D} is non empty set
{E,F,J,M,N} is non empty set
{C,D} \/ {E,F,J,M,N} is non empty set
{A,B} \/ ({C,D} \/ {E,F,J,M,N}) is non empty set
{D,C,E,F,J,M,N} is non empty set
{A,B} \/ {D,C,E,F,J,M,N} is non empty set
{A,B,D,C,E,F,J,M,N} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (E,G) is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' F is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' C) '/\' D) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((A '/\' B) '/\' C) '/\' D) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
{A,B,C} is non empty set
{D,E,F,J,M,N} is non empty set
{A,B,C} \/ {D,E,F,J,M,N} is non empty set
{D,E} is non empty set
{F,J,M,N} is non empty set
{D,E} \/ {F,J,M,N} is non empty set
{A,B,C} \/ ({D,E} \/ {F,J,M,N}) is non empty set
{E,D,F,J,M,N} is non empty set
{A,B,C} \/ {E,D,F,J,M,N} is non empty set
{A,B,C,E,D,F,J,M,N} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (F,G) is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D} is non empty set
{E,F,J,M,N} is non empty set
{A,B,C,D} \/ {E,F,J,M,N} is non empty set
{E,F} is non empty set
{J,M,N} is non empty set
{E,F} \/ {J,M,N} is non empty set
{A,B,C,D} \/ ({E,F} \/ {J,M,N}) is non empty set
{F,E,J,M,N} is non empty set
{A,B,C,D} \/ {F,E,J,M,N} is non empty set
{A,B,C,D,F,E,J,M,N} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (J,G) is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E} is non empty set
{F,J,M,N} is non empty set
{A,B,C,D,E} \/ {F,J,M,N} is non empty set
{J,F} is non empty set
{M,N} is non empty set
{J,F} \/ {M,N} is non empty set
{A,B,C,D,E} \/ ({J,F} \/ {M,N}) is non empty set
{J,F,M,N} is non empty set
{A,B,C,D,E} \/ {J,F,M,N} is non empty set
{A,B,C,D,E,J,F,M,N} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (M,G) is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F} is non empty set
{J,M,N} is non empty set
{A,B,C,D,E,F} \/ {J,M,N} is non empty set
{J,M} is non empty set
{N} is non empty Element of bool (PARTITIONS Y)
{J,M} \/ {N} is non empty set
{A,B,C,D,E,F} \/ ({J,M} \/ {N}) is non empty set
{M,J,N} is non empty set
{A,B,C,D,E,F} \/ {M,J,N} is non empty set
{A,B,C,D,E,F,M,J,N} is non empty set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
CompF (N,G) is non empty with_non-empty_elements a_partition of Y
A '/\' B is non empty with_non-empty_elements a_partition of Y
(A '/\' B) '/\' C is non empty with_non-empty_elements a_partition of Y
((A '/\' B) '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
(((A '/\' B) '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((((A '/\' B) '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J} is non empty set
{M,N} is non empty set
{A,B,C,D,E,F,J} \/ {M,N} is non empty set
{A,B,C,D,E,F,J,N,M} is non empty set
Y is set
G is set
A is set
B is set
C is set
D is set
E is set
F is set
J is set
M is Relation-like Function-like set
M . Y is set
M . G is set
M . A is set
M . B is set
M . C is set
M . D is set
M . E is set
M . F is set
M . J is set
z is set
G .--> z is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> z is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{z}) Element of bool [:{G},{z}:]
{z} is non empty set
[:{G},{z}:] is non empty set
bool [:{G},{z}:] is non empty set
u is set
A .--> u is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> u is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{u}) Element of bool [:{A},{u}:]
{u} is non empty set
[:{A},{u}:] is non empty set
bool [:{A},{u}:] is non empty set
(G .--> z) +* (A .--> u) is Relation-like Function-like set
h is set
B .--> h is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> h is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{h}) Element of bool [:{B},{h}:]
{h} is non empty set
[:{B},{h}:] is non empty set
bool [:{B},{h}:] is non empty set
((G .--> z) +* (A .--> u)) +* (B .--> h) is Relation-like Function-like set
L is set
C .--> L is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> L is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{L}) Element of bool [:{C},{L}:]
{L} is non empty set
[:{C},{L}:] is non empty set
bool [:{C},{L}:] is non empty set
(((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L) is Relation-like Function-like set
GG is set
D .--> GG is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> GG is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{GG}) Element of bool [:{D},{GG}:]
{GG} is non empty set
[:{D},{GG}:] is non empty set
bool [:{D},{GG}:] is non empty set
((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG) is Relation-like Function-like set
I is set
E .--> I is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> I is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{I}) Element of bool [:{E},{I}:]
{I} is non empty set
[:{E},{I}:] is non empty set
bool [:{E},{I}:] is non empty set
(((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I) is Relation-like Function-like set
HH is set
F .--> HH is trivial Relation-like {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> HH is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{HH}) Element of bool [:{F},{HH}:]
{HH} is non empty set
[:{F},{HH}:] is non empty set
bool [:{F},{HH}:] is non empty set
((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH) is Relation-like Function-like set
FF is set
J .--> FF is trivial Relation-like {J} -defined Function-like one-to-one set
{J} is non empty set
{J} --> FF is non empty Relation-like {J} -defined Function-like constant V17({J}) V21({J},{FF}) Element of bool [:{J},{FF}:]
{FF} is non empty set
[:{J},{FF}:] is non empty set
bool [:{J},{FF}:] is non empty set
(((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF) is Relation-like Function-like set
N is set
Y .--> N is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> N is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{N}) Element of bool [:{Y},{N}:]
{N} is non empty set
[:{Y},{N}:] is non empty set
bool [:{Y},{N}:] is non empty set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) +* (Y .--> N) is Relation-like Function-like set
dom (Y .--> N) is set
(Y .--> N) . Y is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . C is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . J is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . B is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . A is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . E is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . D is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . F is set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) . G is set
G is set
A is set
B is set
C is set
D is set
E is set
F is set
J is set
Y is set
{Y,G,A,B,C,D,E,F,J} is non empty set
M is Relation-like Function-like set
dom M is set
z is set
G .--> z is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> z is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{z}) Element of bool [:{G},{z}:]
{z} is non empty set
[:{G},{z}:] is non empty set
bool [:{G},{z}:] is non empty set
u is set
A .--> u is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> u is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{u}) Element of bool [:{A},{u}:]
{u} is non empty set
[:{A},{u}:] is non empty set
bool [:{A},{u}:] is non empty set
(G .--> z) +* (A .--> u) is Relation-like Function-like set
h is set
B .--> h is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> h is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{h}) Element of bool [:{B},{h}:]
{h} is non empty set
[:{B},{h}:] is non empty set
bool [:{B},{h}:] is non empty set
((G .--> z) +* (A .--> u)) +* (B .--> h) is Relation-like Function-like set
L is set
C .--> L is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> L is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{L}) Element of bool [:{C},{L}:]
{L} is non empty set
[:{C},{L}:] is non empty set
bool [:{C},{L}:] is non empty set
(((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L) is Relation-like Function-like set
GG is set
D .--> GG is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> GG is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{GG}) Element of bool [:{D},{GG}:]
{GG} is non empty set
[:{D},{GG}:] is non empty set
bool [:{D},{GG}:] is non empty set
((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG) is Relation-like Function-like set
I is set
E .--> I is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> I is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{I}) Element of bool [:{E},{I}:]
{I} is non empty set
[:{E},{I}:] is non empty set
bool [:{E},{I}:] is non empty set
(((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I) is Relation-like Function-like set
HH is set
F .--> HH is trivial Relation-like {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> HH is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{HH}) Element of bool [:{F},{HH}:]
{HH} is non empty set
[:{F},{HH}:] is non empty set
bool [:{F},{HH}:] is non empty set
((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH) is Relation-like Function-like set
FF is set
J .--> FF is trivial Relation-like {J} -defined Function-like one-to-one set
{J} is non empty set
{J} --> FF is non empty Relation-like {J} -defined Function-like constant V17({J}) V21({J},{FF}) Element of bool [:{J},{FF}:]
{FF} is non empty set
[:{J},{FF}:] is non empty set
bool [:{J},{FF}:] is non empty set
(((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF) is Relation-like Function-like set
N is set
Y .--> N is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> N is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{N}) Element of bool [:{Y},{N}:]
{N} is non empty set
[:{Y},{N}:] is non empty set
bool [:{Y},{N}:] is non empty set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) +* (Y .--> N) is Relation-like Function-like set
dom (Y .--> N) is set
dom ((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) is set
{J,G,A,B,C,D,E,F} is non empty set
{G,A,B,C,D,E,F} is non empty set
{J} \/ {G,A,B,C,D,E,F} is non empty set
{G,A,B,C,D,E,F,J} is non empty set
dom (((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) +* (Y .--> N)) is set
{G,A,B,C,D,E,F,J} \/ {Y} is non empty set
G is set
A is set
B is set
C is set
D is set
E is set
F is set
J is set
Y is set
M is Relation-like Function-like set
rng M is set
M . Y is set
M . G is set
M . A is set
M . B is set
M . C is set
M . D is set
M . E is set
M . F is set
M . J is set
{(M . Y),(M . G),(M . A),(M . B),(M . C),(M . D),(M . E),(M . F),(M . J)} is non empty set
z is set
G .--> z is trivial Relation-like {G} -defined Function-like one-to-one set
{G} is non empty set
{G} --> z is non empty Relation-like {G} -defined Function-like constant V17({G}) V21({G},{z}) Element of bool [:{G},{z}:]
{z} is non empty set
[:{G},{z}:] is non empty set
bool [:{G},{z}:] is non empty set
u is set
A .--> u is trivial Relation-like {A} -defined Function-like one-to-one set
{A} is non empty set
{A} --> u is non empty Relation-like {A} -defined Function-like constant V17({A}) V21({A},{u}) Element of bool [:{A},{u}:]
{u} is non empty set
[:{A},{u}:] is non empty set
bool [:{A},{u}:] is non empty set
(G .--> z) +* (A .--> u) is Relation-like Function-like set
h is set
B .--> h is trivial Relation-like {B} -defined Function-like one-to-one set
{B} is non empty set
{B} --> h is non empty Relation-like {B} -defined Function-like constant V17({B}) V21({B},{h}) Element of bool [:{B},{h}:]
{h} is non empty set
[:{B},{h}:] is non empty set
bool [:{B},{h}:] is non empty set
((G .--> z) +* (A .--> u)) +* (B .--> h) is Relation-like Function-like set
L is set
C .--> L is trivial Relation-like {C} -defined Function-like one-to-one set
{C} is non empty set
{C} --> L is non empty Relation-like {C} -defined Function-like constant V17({C}) V21({C},{L}) Element of bool [:{C},{L}:]
{L} is non empty set
[:{C},{L}:] is non empty set
bool [:{C},{L}:] is non empty set
(((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L) is Relation-like Function-like set
GG is set
D .--> GG is trivial Relation-like {D} -defined Function-like one-to-one set
{D} is non empty set
{D} --> GG is non empty Relation-like {D} -defined Function-like constant V17({D}) V21({D},{GG}) Element of bool [:{D},{GG}:]
{GG} is non empty set
[:{D},{GG}:] is non empty set
bool [:{D},{GG}:] is non empty set
((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG) is Relation-like Function-like set
I is set
E .--> I is trivial Relation-like {E} -defined Function-like one-to-one set
{E} is non empty set
{E} --> I is non empty Relation-like {E} -defined Function-like constant V17({E}) V21({E},{I}) Element of bool [:{E},{I}:]
{I} is non empty set
[:{E},{I}:] is non empty set
bool [:{E},{I}:] is non empty set
(((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I) is Relation-like Function-like set
HH is set
F .--> HH is trivial Relation-like {F} -defined Function-like one-to-one set
{F} is non empty set
{F} --> HH is non empty Relation-like {F} -defined Function-like constant V17({F}) V21({F},{HH}) Element of bool [:{F},{HH}:]
{HH} is non empty set
[:{F},{HH}:] is non empty set
bool [:{F},{HH}:] is non empty set
((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH) is Relation-like Function-like set
FF is set
J .--> FF is trivial Relation-like {J} -defined Function-like one-to-one set
{J} is non empty set
{J} --> FF is non empty Relation-like {J} -defined Function-like constant V17({J}) V21({J},{FF}) Element of bool [:{J},{FF}:]
{FF} is non empty set
[:{J},{FF}:] is non empty set
bool [:{J},{FF}:] is non empty set
(((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF) is Relation-like Function-like set
N is set
Y .--> N is trivial Relation-like {Y} -defined Function-like one-to-one set
{Y} is non empty set
{Y} --> N is non empty Relation-like {Y} -defined Function-like constant V17({Y}) V21({Y},{N}) Element of bool [:{Y},{N}:]
{N} is non empty set
[:{Y},{N}:] is non empty set
bool [:{Y},{N}:] is non empty set
((((((((G .--> z) +* (A .--> u)) +* (B .--> h)) +* (C .--> L)) +* (D .--> GG)) +* (E .--> I)) +* (F .--> HH)) +* (J .--> FF)) +* (Y .--> N) is Relation-like Function-like set
dom M is set
{Y,G,A,B,C,D,E,F,J} is non empty set
m is set
p is set
M . p is set
m is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
u is Element of Y
EqClass (u,(((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)) is Element of ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N
z is Element of Y
EqClass (z,A) is Element of A
(EqClass (u,(((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N))) /\ (EqClass (z,A)) is Element of bool Y
EqClass (u,B) is Element of B
B .--> (EqClass (u,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (u,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (u,B))}) Element of bool [:{B},{(EqClass (u,B))}:]
{(EqClass (u,B))} is non empty set
[:{B},{(EqClass (u,B))}:] is non empty set
bool [:{B},{(EqClass (u,B))}:] is non empty set
EqClass (u,C) is Element of C
C .--> (EqClass (u,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (u,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (u,C))}) Element of bool [:{C},{(EqClass (u,C))}:]
{(EqClass (u,C))} is non empty set
[:{C},{(EqClass (u,C))}:] is non empty set
bool [:{C},{(EqClass (u,C))}:] is non empty set
(B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,D) is Element of D
D .--> (EqClass (u,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (u,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (u,D))}) Element of bool [:{D},{(EqClass (u,D))}:]
{(EqClass (u,D))} is non empty set
[:{D},{(EqClass (u,D))}:] is non empty set
bool [:{D},{(EqClass (u,D))}:] is non empty set
((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,E) is Element of E
E .--> (EqClass (u,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (u,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (u,E))}) Element of bool [:{E},{(EqClass (u,E))}:]
{(EqClass (u,E))} is non empty set
[:{E},{(EqClass (u,E))}:] is non empty set
bool [:{E},{(EqClass (u,E))}:] is non empty set
(((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,F) is Element of F
F .--> (EqClass (u,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (u,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (u,F))}) Element of bool [:{F},{(EqClass (u,F))}:]
{(EqClass (u,F))} is non empty set
[:{F},{(EqClass (u,F))}:] is non empty set
bool [:{F},{(EqClass (u,F))}:] is non empty set
((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,J) is Element of J
J .--> (EqClass (u,J)) is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined J -valued Function-like one-to-one set
{J} is non empty set
{J} --> (EqClass (u,J)) is non empty Relation-like {J} -defined J -valued Function-like constant V17({J}) V21({J},{(EqClass (u,J))}) Element of bool [:{J},{(EqClass (u,J))}:]
{(EqClass (u,J))} is non empty set
[:{J},{(EqClass (u,J))}:] is non empty set
bool [:{J},{(EqClass (u,J))}:] is non empty set
(((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,M) is Element of M
M .--> (EqClass (u,M)) is trivial Relation-like {M} -defined bool (bool Y) -defined {M} -defined M -valued Function-like one-to-one set
{M} is non empty set
{M} --> (EqClass (u,M)) is non empty Relation-like {M} -defined M -valued Function-like constant V17({M}) V21({M},{(EqClass (u,M))}) Element of bool [:{M},{(EqClass (u,M))}:]
{(EqClass (u,M))} is non empty set
[:{M},{(EqClass (u,M))}:] is non empty set
bool [:{M},{(EqClass (u,M))}:] is non empty set
((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,N) is Element of N
N .--> (EqClass (u,N)) is trivial Relation-like {N} -defined bool (bool Y) -defined {N} -defined N -valued Function-like one-to-one set
{N} is non empty set
{N} --> (EqClass (u,N)) is non empty Relation-like {N} -defined N -valued Function-like constant V17({N}) V21({N},{(EqClass (u,N))}) Element of bool [:{N},{(EqClass (u,N))}:]
{(EqClass (u,N))} is non empty set
[:{N},{(EqClass (u,N))}:] is non empty set
bool [:{N},{(EqClass (u,N))}:] is non empty set
(((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N))) is Relation-like bool (bool Y) -defined Function-like set
A .--> (EqClass (z,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (z,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (z,A))}) Element of bool [:{A},{(EqClass (z,A))}:]
{(EqClass (z,A))} is non empty set
[:{A},{(EqClass (z,A))}:] is non empty set
bool [:{A},{(EqClass (z,A))}:] is non empty set
((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A))) is Relation-like bool (bool Y) -defined Function-like set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . A is set
EqClass (u,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of (((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M
(EqClass (u,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)) is Element of ((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J
(EqClass (u,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) /\ (EqClass (u,M)) is Element of bool Y
((EqClass (u,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
(EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (u,J)) is Element of bool Y
((EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
(((EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F)) is Element of bool Y
((EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
(((EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
((((EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E)) is Element of bool Y
((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F)) is Element of bool Y
(((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
((((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
(((((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,(B '/\' C)) is Element of B '/\' C
(EqClass (u,(B '/\' C))) /\ (EqClass (u,D)) is Element of bool Y
((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E)) is Element of bool Y
(((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F)) is Element of bool Y
((((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
(((((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
((((((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
(EqClass (u,B)) /\ (EqClass (u,C)) is Element of bool Y
((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D)) is Element of bool Y
(((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E)) is Element of bool Y
((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F)) is Element of bool Y
(((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
((((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
(((((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
((((((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N))) /\ (EqClass (z,A)) is Element of bool Y
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . B is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . F is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . E is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . M is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . J is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . N is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . D is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . C is set
rng (((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) is set
{((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . A),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . B),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . C),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . D),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . E),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . F),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . J),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . M),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . N)} is non empty set
GG is set
dom (((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) is set
GG is Element of bool (bool Y)
Intersect GG is Element of bool Y
meet (rng (((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A))))) is set
I is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . I is set
I is set
Y is non empty set
PARTITIONS Y is partition-membered Element of bool (bool (bool Y))
bool Y is non empty Element of bool (bool Y)
bool Y is non empty set
bool (bool Y) is non empty set
bool (bool Y) is non empty set
bool (bool (bool Y)) is non empty set
bool (PARTITIONS Y) is non empty set
G is Element of bool (PARTITIONS Y)
A is non empty with_non-empty_elements a_partition of Y
B is non empty with_non-empty_elements a_partition of Y
C is non empty with_non-empty_elements a_partition of Y
D is non empty with_non-empty_elements a_partition of Y
E is non empty with_non-empty_elements a_partition of Y
F is non empty with_non-empty_elements a_partition of Y
J is non empty with_non-empty_elements a_partition of Y
M is non empty with_non-empty_elements a_partition of Y
N is non empty with_non-empty_elements a_partition of Y
{A,B,C,D,E,F,J,M,N} is non empty set
C '/\' D is non empty with_non-empty_elements a_partition of Y
(C '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
((C '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((C '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
(((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
CompF (A,G) is non empty with_non-empty_elements a_partition of Y
CompF (B,G) is non empty with_non-empty_elements a_partition of Y
z is Element of Y
EqClass (z,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)) is Element of (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N
u is Element of Y
EqClass (u,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)) is Element of (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N
EqClass (u,(CompF (A,G))) is Element of CompF (A,G)
EqClass (z,(CompF (B,G))) is Element of CompF (B,G)
EqClass (u,B) is Element of B
B .--> (EqClass (u,B)) is trivial Relation-like {B} -defined bool (bool Y) -defined {B} -defined B -valued Function-like one-to-one set
{B} is non empty set
{B} --> (EqClass (u,B)) is non empty Relation-like {B} -defined B -valued Function-like constant V17({B}) V21({B},{(EqClass (u,B))}) Element of bool [:{B},{(EqClass (u,B))}:]
{(EqClass (u,B))} is non empty set
[:{B},{(EqClass (u,B))}:] is non empty set
bool [:{B},{(EqClass (u,B))}:] is non empty set
EqClass (u,C) is Element of C
C .--> (EqClass (u,C)) is trivial Relation-like {C} -defined bool (bool Y) -defined {C} -defined C -valued Function-like one-to-one set
{C} is non empty set
{C} --> (EqClass (u,C)) is non empty Relation-like {C} -defined C -valued Function-like constant V17({C}) V21({C},{(EqClass (u,C))}) Element of bool [:{C},{(EqClass (u,C))}:]
{(EqClass (u,C))} is non empty set
[:{C},{(EqClass (u,C))}:] is non empty set
bool [:{C},{(EqClass (u,C))}:] is non empty set
(B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,D) is Element of D
D .--> (EqClass (u,D)) is trivial Relation-like {D} -defined bool (bool Y) -defined {D} -defined D -valued Function-like one-to-one set
{D} is non empty set
{D} --> (EqClass (u,D)) is non empty Relation-like {D} -defined D -valued Function-like constant V17({D}) V21({D},{(EqClass (u,D))}) Element of bool [:{D},{(EqClass (u,D))}:]
{(EqClass (u,D))} is non empty set
[:{D},{(EqClass (u,D))}:] is non empty set
bool [:{D},{(EqClass (u,D))}:] is non empty set
((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,E) is Element of E
E .--> (EqClass (u,E)) is trivial Relation-like {E} -defined bool (bool Y) -defined {E} -defined E -valued Function-like one-to-one set
{E} is non empty set
{E} --> (EqClass (u,E)) is non empty Relation-like {E} -defined E -valued Function-like constant V17({E}) V21({E},{(EqClass (u,E))}) Element of bool [:{E},{(EqClass (u,E))}:]
{(EqClass (u,E))} is non empty set
[:{E},{(EqClass (u,E))}:] is non empty set
bool [:{E},{(EqClass (u,E))}:] is non empty set
(((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,F) is Element of F
F .--> (EqClass (u,F)) is trivial Relation-like {F} -defined bool (bool Y) -defined {F} -defined F -valued Function-like one-to-one set
{F} is non empty set
{F} --> (EqClass (u,F)) is non empty Relation-like {F} -defined F -valued Function-like constant V17({F}) V21({F},{(EqClass (u,F))}) Element of bool [:{F},{(EqClass (u,F))}:]
{(EqClass (u,F))} is non empty set
[:{F},{(EqClass (u,F))}:] is non empty set
bool [:{F},{(EqClass (u,F))}:] is non empty set
((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,J) is Element of J
J .--> (EqClass (u,J)) is trivial Relation-like {J} -defined bool (bool Y) -defined {J} -defined J -valued Function-like one-to-one set
{J} is non empty set
{J} --> (EqClass (u,J)) is non empty Relation-like {J} -defined J -valued Function-like constant V17({J}) V21({J},{(EqClass (u,J))}) Element of bool [:{J},{(EqClass (u,J))}:]
{(EqClass (u,J))} is non empty set
[:{J},{(EqClass (u,J))}:] is non empty set
bool [:{J},{(EqClass (u,J))}:] is non empty set
(((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,M) is Element of M
M .--> (EqClass (u,M)) is trivial Relation-like {M} -defined bool (bool Y) -defined {M} -defined M -valued Function-like one-to-one set
{M} is non empty set
{M} --> (EqClass (u,M)) is non empty Relation-like {M} -defined M -valued Function-like constant V17({M}) V21({M},{(EqClass (u,M))}) Element of bool [:{M},{(EqClass (u,M))}:]
{(EqClass (u,M))} is non empty set
[:{M},{(EqClass (u,M))}:] is non empty set
bool [:{M},{(EqClass (u,M))}:] is non empty set
((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (u,N) is Element of N
N .--> (EqClass (u,N)) is trivial Relation-like {N} -defined bool (bool Y) -defined {N} -defined N -valued Function-like one-to-one set
{N} is non empty set
{N} --> (EqClass (u,N)) is non empty Relation-like {N} -defined N -valued Function-like constant V17({N}) V21({N},{(EqClass (u,N))}) Element of bool [:{N},{(EqClass (u,N))}:]
{(EqClass (u,N))} is non empty set
[:{N},{(EqClass (u,N))}:] is non empty set
bool [:{N},{(EqClass (u,N))}:] is non empty set
(((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N))) is Relation-like bool (bool Y) -defined Function-like set
EqClass (z,A) is Element of A
A .--> (EqClass (z,A)) is trivial Relation-like {A} -defined bool (bool Y) -defined {A} -defined A -valued Function-like one-to-one set
{A} is non empty set
{A} --> (EqClass (z,A)) is non empty Relation-like {A} -defined A -valued Function-like constant V17({A}) V21({A},{(EqClass (z,A))}) Element of bool [:{A},{(EqClass (z,A))}:]
{(EqClass (z,A))} is non empty set
[:{A},{(EqClass (z,A))}:] is non empty set
bool [:{A},{(EqClass (z,A))}:] is non empty set
((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A))) is Relation-like bool (bool Y) -defined Function-like set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . A is set
B '/\' C is non empty with_non-empty_elements a_partition of Y
(B '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((B '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((B '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
EqClass (u,(((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)) is Element of ((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N
EqClass (u,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) is Element of (((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M
(EqClass (u,((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J)) is Element of ((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J
(EqClass (u,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) /\ (EqClass (u,M)) is Element of bool Y
((EqClass (u,(((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F)) is Element of (((B '/\' C) '/\' D) '/\' E) '/\' F
(EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (u,J)) is Element of bool Y
((EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
(((EqClass (u,((((B '/\' C) '/\' D) '/\' E) '/\' F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,(((B '/\' C) '/\' D) '/\' E)) is Element of ((B '/\' C) '/\' D) '/\' E
(EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F)) is Element of bool Y
((EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
(((EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
((((EqClass (u,(((B '/\' C) '/\' D) '/\' E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,((B '/\' C) '/\' D)) is Element of (B '/\' C) '/\' D
(EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E)) is Element of bool Y
((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F)) is Element of bool Y
(((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
((((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
(((((EqClass (u,((B '/\' C) '/\' D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
EqClass (u,(B '/\' C)) is Element of B '/\' C
(EqClass (u,(B '/\' C))) /\ (EqClass (u,D)) is Element of bool Y
((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E)) is Element of bool Y
(((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F)) is Element of bool Y
((((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
(((((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
((((((EqClass (u,(B '/\' C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
I is set
(EqClass (u,(((((((B '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N))) /\ I is Element of bool Y
(EqClass (u,B)) /\ (EqClass (u,C)) is Element of bool Y
((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D)) is Element of bool Y
(((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E)) is Element of bool Y
((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F)) is Element of bool Y
(((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J)) is Element of bool Y
((((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M)) is Element of bool Y
(((((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N)) is Element of bool Y
((((((((EqClass (u,B)) /\ (EqClass (u,C))) /\ (EqClass (u,D))) /\ (EqClass (u,E))) /\ (EqClass (u,F))) /\ (EqClass (u,J))) /\ (EqClass (u,M))) /\ (EqClass (u,N))) /\ (EqClass (z,A)) is Element of bool Y
HH is set
A '/\' ((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N) is non empty with_non-empty_elements a_partition of Y
A '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) is non empty with_non-empty_elements a_partition of Y
(A '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) '/\' N is non empty with_non-empty_elements a_partition of Y
A '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J) is non empty with_non-empty_elements a_partition of Y
(A '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M is non empty with_non-empty_elements a_partition of Y
((A '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
A '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
(A '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J is non empty with_non-empty_elements a_partition of Y
((A '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
(((A '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
A '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(A '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
((A '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((A '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((A '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
A '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(A '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((A '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((A '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((A '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
(((((A '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
A '/\' C is non empty with_non-empty_elements a_partition of Y
(A '/\' C) '/\' D is non empty with_non-empty_elements a_partition of Y
((A '/\' C) '/\' D) '/\' E is non empty with_non-empty_elements a_partition of Y
(((A '/\' C) '/\' D) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((((A '/\' C) '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . B is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . N is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . D is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . C is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . M is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . J is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . F is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . E is set
rng (((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) is set
{((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . A),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . B),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . C),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . D),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . E),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . F),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . J),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . M),((((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . N)} is non empty set
FF is set
dom (((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) is set
FF is Element of bool (bool Y)
Intersect FF is Element of bool Y
meet (rng (((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A))))) is set
m is set
(((((((((B .--> (EqClass (u,B))) +* (C .--> (EqClass (u,C)))) +* (D .--> (EqClass (u,D)))) +* (E .--> (EqClass (u,E)))) +* (F .--> (EqClass (u,F)))) +* (J .--> (EqClass (u,J)))) +* (M .--> (EqClass (u,M)))) +* (N .--> (EqClass (u,N)))) +* (A .--> (EqClass (z,A)))) . m is set
m is set
p is set
p is Element of Y
EqClass (p,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)) is Element of (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N
B '/\' (C '/\' D) is non empty with_non-empty_elements a_partition of Y
(B '/\' (C '/\' D)) '/\' E is non empty with_non-empty_elements a_partition of Y
((B '/\' (C '/\' D)) '/\' E) '/\' F is non empty with_non-empty_elements a_partition of Y
(((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
(((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
EqClass (u,((((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)) is Element of (((((B '/\' (C '/\' D)) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N
B '/\' ((C '/\' D) '/\' E) is non empty with_non-empty_elements a_partition of Y
(B '/\' ((C '/\' D) '/\' E)) '/\' F is non empty with_non-empty_elements a_partition of Y
((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J is non empty with_non-empty_elements a_partition of Y
(((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
((((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
EqClass (u,(((((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M) '/\' N)) is Element of ((((B '/\' ((C '/\' D) '/\' E)) '/\' F) '/\' J) '/\' M) '/\' N
B '/\' (((C '/\' D) '/\' E) '/\' F) is non empty with_non-empty_elements a_partition of Y
(B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J is non empty with_non-empty_elements a_partition of Y
((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M is non empty with_non-empty_elements a_partition of Y
(((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
EqClass (u,((((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M) '/\' N)) is Element of (((B '/\' (((C '/\' D) '/\' E) '/\' F)) '/\' J) '/\' M) '/\' N
B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J) is non empty with_non-empty_elements a_partition of Y
(B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M is non empty with_non-empty_elements a_partition of Y
((B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M) '/\' N is non empty with_non-empty_elements a_partition of Y
EqClass (u,(((B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M) '/\' N)) is Element of ((B '/\' ((((C '/\' D) '/\' E) '/\' F) '/\' J)) '/\' M) '/\' N
B '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) is non empty with_non-empty_elements a_partition of Y
(B '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) '/\' N is non empty with_non-empty_elements a_partition of Y
EqClass (u,((B '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) '/\' N)) is Element of (B '/\' (((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M)) '/\' N
B '/\' ((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N) is non empty with_non-empty_elements a_partition of Y
EqClass (u,(B '/\' ((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N))) is Element of B '/\' ((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)
I /\ (EqClass (p,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N))) is Element of bool Y
INTERSECTION (A,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)) is set
(INTERSECTION (A,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N))) \ {{}} is Element of bool (INTERSECTION (A,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N)))
bool (INTERSECTION (A,((((((C '/\' D) '/\' E) '/\' F) '/\' J) '/\' M) '/\' N))) is non empty set