:: MEMBER_1 semantic presentation

REAL is complex-membered ext-real-membered real-membered V21() set
NAT is non empty epsilon-transitive epsilon-connected ordinal complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() Element of K13(REAL)
K13(REAL) is set
COMPLEX is complex-membered V21() set
RAT is complex-membered ext-real-membered real-membered rational-membered V21() set
INT is complex-membered ext-real-membered real-membered rational-membered integer-membered V21() set
K14(COMPLEX,COMPLEX) is set
K13(K14(COMPLEX,COMPLEX)) is set
K14(K14(COMPLEX,COMPLEX),COMPLEX) is set
K13(K14(K14(COMPLEX,COMPLEX),COMPLEX)) is set
K14(REAL,REAL) is set
K13(K14(REAL,REAL)) is set
K14(K14(REAL,REAL),REAL) is set
K13(K14(K14(REAL,REAL),REAL)) is set
K14(RAT,RAT) is set
K13(K14(RAT,RAT)) is set
K14(K14(RAT,RAT),RAT) is set
K13(K14(K14(RAT,RAT),RAT)) is set
K14(INT,INT) is set
K13(K14(INT,INT)) is set
K14(K14(INT,INT),INT) is set
K13(K14(K14(INT,INT),INT)) is set
K14(NAT,NAT) is set
K14(K14(NAT,NAT),NAT) is set
K13(K14(K14(NAT,NAT),NAT)) is set
0 is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative Element of NAT
the complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
ExtREAL is ext-real-membered set
+infty is non real set
-infty is non real set
A is ext-real Element of ExtREAL
- A is ext-real set
A " is ext-real set
B is ext-real Element of ExtREAL
A * B is ext-real set
A is complex set
B is complex set
a is complex set
z is complex set
{A,B,a,z} is set
c2 is set
A is ext-real set
B is ext-real set
a is ext-real set
z is ext-real set
{A,B,a,z} is set
c2 is set
A is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is set
a is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
B is ext-real-membered set
a is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
z is ext-real set
- z is ext-real set
- (- z) is ext-real set
z is set
c2 is ext-real Element of ExtREAL
(c2) is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(w3) is ext-real Element of ExtREAL
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real set
- B is ext-real set
- (- B) is ext-real set
a is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real set
- B is ext-real set
- (- B) is ext-real set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
the ext-real Element of (A) is ext-real Element of (A)
B is ext-real Element of ExtREAL
(B) is ext-real Element of ExtREAL
A is non empty ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
the ext-real Element of A is ext-real Element of A
- the ext-real Element of A is ext-real set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
a is ext-real set
- a is ext-real set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
((A)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A) } is set
((B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (B) } is set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
A \/ B is ext-real-membered set
((A \/ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \/ B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A) \/ (B) is ext-real-membered set
a is ext-real set
- a is ext-real set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
A /\ B is ext-real-membered set
((A /\ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A /\ B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A) /\ (B) is ext-real-membered set
a is ext-real set
- a is ext-real set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
((A \ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \ B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A) \ (B) is ext-real-membered Element of K13((A))
K13((A)) is set
a is ext-real set
- a is ext-real set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
A \+\ B is ext-real-membered set
A \ B is ext-real-membered set
B \ A is ext-real-membered set
(A \ B) \/ (B \ A) is ext-real-membered set
((A \+\ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \+\ B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A) \+\ (B) is ext-real-membered set
(A) \ (B) is ext-real-membered set
(B) \ (A) is ext-real-membered set
((A) \ (B)) \/ ((B) \ (A)) is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
((A \ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \ B } is set
B \ A is ext-real-membered Element of K13(B)
K13(B) is set
((B \ A)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B \ A } is set
((A \ B)) \/ ((B \ A)) is ext-real-membered set
(A) \ (B) is ext-real-membered Element of K13((A))
K13((A)) is set
((A) \ (B)) \/ ((B \ A)) is ext-real-membered set
A is ext-real set
{A} is non empty ext-real-membered set
({A}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A} } is set
- A is ext-real set
{(- A)} is non empty ext-real-membered set
B is ext-real set
a is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
A is ext-real set
- A is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
({A,B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A,B} } is set
- B is ext-real set
{(- A),(- B)} is non empty ext-real-membered set
{A} is non empty ext-real-membered set
{B} is non empty ext-real-membered set
{A} \/ {B} is non empty ext-real-membered set
(({A} \/ {B})) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A} \/ {B} } is set
({A}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A} } is set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
({A}) \/ ({B}) is non empty ext-real-membered set
{(- A)} is non empty ext-real-membered set
{(- A)} \/ ({B}) is non empty ext-real-membered set
{(- B)} is non empty ext-real-membered set
{(- A)} \/ {(- B)} is non empty ext-real-membered set
A is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is set
a is complex Element of COMPLEX
- a is complex Element of COMPLEX
B is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
a is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
z is complex set
- z is complex Element of COMPLEX
- (- z) is complex Element of COMPLEX
z is set
c2 is complex Element of COMPLEX
- c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
- w3 is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex set
- B is complex Element of COMPLEX
a is complex Element of COMPLEX
- a is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex set
- B is complex Element of COMPLEX
- (- B) is complex Element of COMPLEX
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
the complex Element of (A) is complex Element of (A)
B is complex Element of COMPLEX
- B is complex Element of COMPLEX
A is non empty complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
the complex Element of A is complex Element of A
- the complex Element of A is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is set
a is complex Element of COMPLEX
- a is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is set
a is complex Element of COMPLEX
- a is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
(A) is complex-membered ext-real-membered real-membered rational-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is set
a is complex Element of COMPLEX
- a is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
a is ext-real set
z is complex real ext-real set
- z is complex real ext-real set
- z is complex real ext-real set
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
c2 is complex real ext-real set
- c2 is complex real ext-real set
- c2 is complex real ext-real set
- a is ext-real set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
a is complex set
- a is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
((A)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A) } is set
((B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B) } is set
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A \/ B is complex-membered set
((A \/ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \/ B } is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) \/ (B) is complex-membered set
a is complex set
- a is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A /\ B is complex-membered set
((A /\ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A /\ B } is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) /\ (B) is complex-membered set
a is complex set
- a is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
((A \ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \ B } is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) \ (B) is complex-membered Element of K13((A))
K13((A)) is set
a is complex set
- a is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
((A \+\ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \+\ B } is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) \+\ (B) is complex-membered set
(A) \ (B) is complex-membered set
(B) \ (A) is complex-membered set
((A) \ (B)) \/ ((B) \ (A)) is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
((A \ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \ B } is set
B \ A is complex-membered Element of K13(B)
K13(B) is set
((B \ A)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B \ A } is set
((A \ B)) \/ ((B \ A)) is complex-membered set
(A) \ (B) is complex-membered Element of K13((A))
K13((A)) is set
((A) \ (B)) \/ ((B \ A)) is complex-membered set
A is complex set
{A} is non empty complex-membered set
({A}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {A} } is set
- A is complex Element of COMPLEX
{(- A)} is non empty complex-membered set
B is complex set
a is complex Element of COMPLEX
- a is complex Element of COMPLEX
A is complex set
- A is complex Element of COMPLEX
B is complex set
{A,B} is non empty complex-membered set
({A,B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {A,B} } is set
- B is complex Element of COMPLEX
{(- A),(- B)} is non empty complex-membered set
{A} is non empty complex-membered set
{B} is non empty complex-membered set
{A} \/ {B} is non empty complex-membered set
(({A} \/ {B})) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {A} \/ {B} } is set
({A}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {A} } is set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({A}) \/ ({B}) is non empty complex-membered set
{(- A)} is non empty complex-membered set
{(- A)} \/ ({B}) is non empty complex-membered set
{(- B)} is non empty complex-membered set
{(- A)} \/ {(- B)} is non empty complex-membered set
A is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is set
a is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real set
B " is ext-real set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
the ext-real Element of (A) is ext-real Element of (A)
B is ext-real Element of ExtREAL
(B) is ext-real Element of ExtREAL
A is non empty ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
the ext-real Element of A is ext-real Element of A
the ext-real Element of A " is ext-real set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
a is ext-real set
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
A \/ B is ext-real-membered set
((A \/ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \/ B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A) \/ (B) is ext-real-membered set
a is ext-real set
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
A /\ B is ext-real-membered set
((A /\ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A /\ B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A) /\ (B) is ext-real-membered set
a is ext-real set
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
((A)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A) } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
((A)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A) } is set
B is ext-real set
- B is ext-real set
a is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
((a)) is ext-real Element of ExtREAL
((a)) is ext-real Element of ExtREAL
a is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
((a)) is ext-real Element of ExtREAL
((a)) is ext-real Element of ExtREAL
A is ext-real set
{A} is non empty ext-real-membered set
({A}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A} } is set
A " is ext-real set
{(A ")} is non empty ext-real-membered set
B is ext-real set
a is ext-real Element of ExtREAL
(a) is ext-real Element of ExtREAL
A is ext-real set
A " is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
({A,B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A,B} } is set
B " is ext-real set
{(A "),(B ")} is non empty ext-real-membered set
{A} is non empty ext-real-membered set
{B} is non empty ext-real-membered set
{A} \/ {B} is non empty ext-real-membered set
(({A} \/ {B})) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A} \/ {B} } is set
({A}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {A} } is set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
({A}) \/ ({B}) is non empty ext-real-membered set
{(A ")} is non empty ext-real-membered set
{(A ")} \/ ({B}) is non empty ext-real-membered set
{(B ")} is non empty ext-real-membered set
{(A ")} \/ {(B ")} is non empty ext-real-membered set
A is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is set
a is complex Element of COMPLEX
a " is complex Element of COMPLEX
B is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
a is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
z is complex set
z " is complex Element of COMPLEX
(z ") " is complex Element of COMPLEX
z is set
c2 is complex Element of COMPLEX
c2 " is complex Element of COMPLEX
w3 is complex Element of COMPLEX
w3 " is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex set
B " is complex Element of COMPLEX
a is complex Element of COMPLEX
a " is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex set
B " is complex Element of COMPLEX
(B ") " is complex Element of COMPLEX
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
the complex Element of (A) is complex Element of (A)
B is complex Element of COMPLEX
B " is complex Element of COMPLEX
A is non empty complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
the complex Element of A is complex Element of A
the complex Element of A " is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is set
a is complex Element of COMPLEX
a " is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is set
a is complex Element of COMPLEX
a " is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
a is ext-real set
z is complex Element of COMPLEX
z " is complex Element of COMPLEX
c2 is ext-real Element of ExtREAL
(c2) is ext-real Element of ExtREAL
w3 is complex set
w3 " is complex Element of COMPLEX
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
c2 is complex Element of COMPLEX
c2 " is complex Element of COMPLEX
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
a is complex set
a " is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
((A)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (A) } is set
((B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (B) } is set
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A \/ B is complex-membered set
((A \/ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A \/ B } is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) \/ (B) is complex-membered set
a is complex set
a " is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A /\ B is complex-membered set
((A /\ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A /\ B } is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) /\ (B) is complex-membered set
a is complex set
a " is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
((A \ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A \ B } is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) \ (B) is complex-membered Element of K13((A))
K13((A)) is set
a is complex set
a " is complex Element of COMPLEX
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
((A \+\ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A \+\ B } is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A) \+\ (B) is complex-membered set
(A) \ (B) is complex-membered set
(B) \ (A) is complex-membered set
((A) \ (B)) \/ ((B) \ (A)) is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
((A \ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A \ B } is set
B \ A is complex-membered Element of K13(B)
K13(B) is set
((B \ A)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B \ A } is set
((A \ B)) \/ ((B \ A)) is complex-membered set
(A) \ (B) is complex-membered Element of K13((A))
K13((A)) is set
((A) \ (B)) \/ ((B \ A)) is complex-membered set
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
((A)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A) } is set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
((A)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (A) } is set
B is complex set
- B is complex Element of COMPLEX
(- B) " is complex Element of COMPLEX
B " is complex Element of COMPLEX
- (B ") is complex Element of COMPLEX
A is complex set
{A} is non empty complex-membered set
({A}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {A} } is set
A " is complex Element of COMPLEX
{(A ")} is non empty complex-membered set
B is complex set
a is complex Element of COMPLEX
a " is complex Element of COMPLEX
A is complex set
A " is complex Element of COMPLEX
B is complex set
{A,B} is non empty complex-membered set
({A,B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {A,B} } is set
B " is complex Element of COMPLEX
{(A "),(B ")} is non empty complex-membered set
a is complex set
z is complex Element of COMPLEX
z " is complex Element of COMPLEX
A is ext-real-membered set
B is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is set
z is ext-real-membered set
c2 is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in z & b₂ in c2 ) } is set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in c2 & b₂ in z ) } is set
w3 is set
c3 is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
c3 + c2 is ext-real set
w3 is set
c3 is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
c3 + c2 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real set
z is ext-real set
a + z is ext-real set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
the Element of (A,B) is Element of (A,B)
a is ext-real Element of ExtREAL
z is ext-real Element of ExtREAL
a + z is ext-real set
(B,A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in A ) } is set
A is non empty ext-real-membered set
B is non empty ext-real-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
the ext-real Element of A is ext-real Element of A
the ext-real Element of B is ext-real Element of B
the ext-real Element of A + the ext-real Element of B is ext-real set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z + c2 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
a is ext-real-membered set
(A,a) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
z is ext-real-membered set
(B,z) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in z ) } is set
c2 is ext-real set
w3 is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
w3 + c3 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real-membered set
B \/ a is ext-real-membered set
(A,(B \/ a)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B \/ a ) } is set
(A,a) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
(A,B) \/ (A,a) is ext-real-membered set
z is ext-real set
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
c2 + w3 is ext-real set
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
c2 + w3 is ext-real set
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
c2 + w3 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real-membered set
B /\ a is ext-real-membered set
(A,(B /\ a)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B /\ a ) } is set
(A,a) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
(A,B) /\ (A,a) is ext-real-membered set
z is ext-real set
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
c2 + w3 is ext-real set
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
{B} is non empty ext-real-membered set
({A},{B}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B} ) } is set
A + B is ext-real set
{(A + B)} is non empty ext-real-membered set
a is ext-real set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z + c2 is ext-real set
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
A + B is ext-real set
a is ext-real set
{B,a} is non empty ext-real-membered set
({A},{B,a}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B,a} ) } is set
A + a is ext-real set
{(A + B),(A + a)} is non empty ext-real-membered set
{B} is non empty ext-real-membered set
{a} is non empty ext-real-membered set
{B} \/ {a} is non empty ext-real-membered set
({A},({B} \/ {a})) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B} \/ {a} ) } is set
({A},{B}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B} ) } is set
({A},{a}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {a} ) } is set
({A},{B}) \/ ({A},{a}) is non empty ext-real-membered set
{(A + B)} is non empty ext-real-membered set
{(A + B)} \/ ({A},{a}) is non empty ext-real-membered set
{(A + a)} is non empty ext-real-membered set
{(A + B)} \/ {(A + a)} is non empty ext-real-membered set
A is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
a is ext-real set
A + a is ext-real set
B + a is ext-real set
z is ext-real set
{a,z} is non empty ext-real-membered set
({A,B},{a,z}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in {a,z} ) } is set
A + z is ext-real set
B + z is ext-real set
{(A + a),(A + z),(B + a),(B + z)} is ext-real-membered set
{A} is non empty ext-real-membered set
{B} is non empty ext-real-membered set
{A} \/ {B} is non empty ext-real-membered set
(({A} \/ {B}),{a,z}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} \/ {B} & b₂ in {a,z} ) } is set
({A},{a,z}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {a,z} ) } is set
({B},{a,z}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in {a,z} ) } is set
({A},{a,z}) \/ ({B},{a,z}) is non empty ext-real-membered set
{(A + a),(A + z)} is non empty ext-real-membered set
{(A + a),(A + z)} \/ ({B},{a,z}) is non empty ext-real-membered set
{(B + a),(B + z)} is non empty ext-real-membered set
{(A + a),(A + z)} \/ {(B + a),(B + z)} is non empty ext-real-membered set
A is complex-membered set
B is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex-membered set
c2 is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in z & b₂ in c2 ) } is set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in c2 & b₂ in z ) } is set
w3 is set
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 + c2 is complex Element of COMPLEX
w3 is set
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 + c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex set
z is complex set
a + z is complex Element of COMPLEX
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
the Element of (A,B) is Element of (A,B)
a is complex Element of COMPLEX
z is complex Element of COMPLEX
a + z is complex Element of COMPLEX
(B,A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in A ) } is set
A is non empty complex-membered set
B is non empty complex-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
the complex Element of A is complex Element of A
the complex Element of B is complex Element of B
the complex Element of A + the complex Element of B is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
B is complex-membered ext-real-membered real-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex-membered ext-real-membered real-membered rational-membered set
(A,B) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
B is complex-membered ext-real-membered real-membered rational-membered integer-membered set
(A,B) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
B is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
(A,B) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
a is ext-real-membered set
B is complex-membered ext-real-membered real-membered set
z is ext-real-membered set
(A,B) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
(a,z) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in a & b₂ in z ) } is set
c2 is ext-real set
w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
w3 + c3 is complex Element of COMPLEX
c2 is ext-real Element of ExtREAL
d2 is ext-real Element of ExtREAL
c2 + d2 is ext-real set
w3 is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
w3 + c3 is ext-real set
c2 is complex Element of COMPLEX
d2 is complex Element of COMPLEX
c2 + d2 is complex Element of COMPLEX
(A,B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
A is complex-membered set
B is complex-membered set
a is complex-membered set
(A,a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
z is complex-membered set
(B,z) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in z ) } is set
c2 is complex set
w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
w3 + c3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
B \/ a is complex-membered set
(A,(B \/ a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B \/ a ) } is set
(A,a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
(A,B) \/ (A,a) is complex-membered set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
B /\ a is complex-membered set
(A,(B /\ a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B /\ a ) } is set
(A,a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
(A,B) /\ (A,a) is complex-membered set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
((A,B),a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in a ) } is set
(B,a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in a ) } is set
(A,(B,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B,a) ) } is set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 + c2 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
c3 + (c2 + w3) is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 + c2 is complex Element of COMPLEX
c2 + c3 is complex Element of COMPLEX
(c2 + c3) + c2 is complex Element of COMPLEX
A is complex set
{A} is non empty complex-membered set
B is complex set
{B} is non empty complex-membered set
({A},{B}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B} ) } is set
A + B is complex Element of COMPLEX
{(A + B)} is non empty complex-membered set
a is complex set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
A is complex set
{A} is non empty complex-membered set
B is complex set
A + B is complex Element of COMPLEX
a is complex set
{B,a} is non empty complex-membered set
({A},{B,a}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B,a} ) } is set
A + a is complex Element of COMPLEX
{(A + B),(A + a)} is non empty complex-membered set
{B} is non empty complex-membered set
{a} is non empty complex-membered set
{B} \/ {a} is non empty complex-membered set
({A},({B} \/ {a})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B} \/ {a} ) } is set
({A},{B}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B} ) } is set
({A},{a}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {a} ) } is set
({A},{B}) \/ ({A},{a}) is non empty complex-membered set
{(A + B)} is non empty complex-membered set
{(A + B)} \/ ({A},{a}) is non empty complex-membered set
{(A + a)} is non empty complex-membered set
{(A + B)} \/ {(A + a)} is non empty complex-membered set
A is complex set
B is complex set
{A,B} is non empty complex-membered set
a is complex set
A + a is complex Element of COMPLEX
B + a is complex Element of COMPLEX
z is complex set
{a,z} is non empty complex-membered set
({A,B},{a,z}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in {a,z} ) } is set
A + z is complex Element of COMPLEX
B + z is complex Element of COMPLEX
{(A + a),(A + z),(B + a),(B + z)} is complex-membered set
{A} is non empty complex-membered set
{B} is non empty complex-membered set
{A} \/ {B} is non empty complex-membered set
(({A} \/ {B}),{a,z}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} \/ {B} & b₂ in {a,z} ) } is set
({A},{a,z}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {a,z} ) } is set
({B},{a,z}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in {a,z} ) } is set
({A},{a,z}) \/ ({B},{a,z}) is non empty complex-membered set
{(A + a),(A + z)} is non empty complex-membered set
{(A + a),(A + z)} \/ ({B},{a,z}) is non empty complex-membered set
{(B + a),(B + z)} is non empty complex-membered set
{(A + a),(A + z)} \/ {(B + a),(B + z)} is non empty complex-membered set
A is ext-real-membered set
B is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
{ (b₁ - b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z + c2 is ext-real set
(c2) is ext-real Element of ExtREAL
z - (c2) is ext-real set
- (c2) is ext-real set
z + (- (c2)) is ext-real set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z - c2 is ext-real set
- c2 is ext-real set
z + (- c2) is ext-real set
(c2) is ext-real Element of ExtREAL
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real set
z is ext-real set
a - z is ext-real set
- z is ext-real set
a + (- z) is ext-real set
{ (b₁ - b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
(B,A) is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
(B,(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in (A) ) } is set
A is non empty ext-real-membered set
B is non empty ext-real-membered set
(A,B) is set
(B) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
a is ext-real-membered set
(A,a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
(A,(a)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
z is ext-real-membered set
(B,z) is ext-real-membered set
(z) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in z } is set
(B,(z)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in (z) ) } is set
c2 is ext-real set
{ (b₁ - b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
w3 is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
w3 - c3 is ext-real set
- c3 is ext-real set
w3 + (- c3) is ext-real set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real-membered set
B \/ a is ext-real-membered set
(A,(B \/ a)) is ext-real-membered set
((B \/ a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B \/ a } is set
(A,((B \/ a))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ((B \/ a)) ) } is set
(A,a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
(A,(a)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
(A,B) \/ (A,a) is ext-real-membered set
(B) \/ (a) is ext-real-membered set
(A,((B) \/ (a))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) \/ (a) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real-membered set
B /\ a is ext-real-membered set
(A,(B /\ a)) is ext-real-membered set
((B /\ a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B /\ a } is set
(A,((B /\ a))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ((B /\ a)) ) } is set
(A,a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
(A,(a)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
(A,B) /\ (A,a) is ext-real-membered set
(B) /\ (a) is ext-real-membered set
(A,((B) /\ (a))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) /\ (a) ) } is set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
((A,B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,B) } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
((A),(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A) & b₂ in (B) ) } is set
a is ext-real set
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
c2 + w3 is ext-real set
- (c2 + w3) is ext-real set
(c2) is ext-real Element of ExtREAL
(c2) - w3 is ext-real set
- w3 is ext-real set
(c2) + (- w3) is ext-real set
(w3) is ext-real Element of ExtREAL
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z + c2 is ext-real set
(z) is ext-real Element of ExtREAL
(c2) is ext-real Element of ExtREAL
- (z + c2) is ext-real set
(z) - c2 is ext-real set
- c2 is ext-real set
(z) + (- c2) is ext-real set
(z) + (c2) is ext-real set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
((A,B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,B) } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
((A),B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
((A),(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A) & b₂ in (B) ) } is set
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
(A,B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
((A,B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,B) } is set
((A),B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A) & b₂ in B ) } is set
((A),(B)) is ext-real-membered set
((B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (B) } is set
((A),((B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A) & b₂ in ((B)) ) } is set
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
{B} is non empty ext-real-membered set
({A},{B}) is non empty ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
({A},({B})) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in ({B}) ) } is set
A - B is ext-real set
- B is ext-real set
A + (- B) is ext-real set
{(A - B)} is non empty ext-real-membered set
{(- B)} is non empty ext-real-membered set
({A},{(- B)}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {(- B)} ) } is set
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
A - B is ext-real set
- B is ext-real set
A + (- B) is ext-real set
a is ext-real set
{B,a} is non empty ext-real-membered set
({A},{B,a}) is non empty ext-real-membered set
({B,a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B,a} } is set
({A},({B,a})) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in ({B,a}) ) } is set
A - a is ext-real set
- a is ext-real set
A + (- a) is ext-real set
{(A - B),(A - a)} is non empty ext-real-membered set
{(- B),(- a)} is non empty ext-real-membered set
({A},{(- B),(- a)}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {(- B),(- a)} ) } is set
A is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
a is ext-real set
{a} is non empty ext-real-membered set
({A,B},{a}) is non empty ext-real-membered set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
({A,B},({a})) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in ({a}) ) } is set
A - a is ext-real set
- a is ext-real set
A + (- a) is ext-real set
B - a is ext-real set
B + (- a) is ext-real set
{(A - a),(B - a)} is non empty ext-real-membered set
{(- a)} is non empty ext-real-membered set
({A,B},{(- a)}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in {(- a)} ) } is set
A is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
a is ext-real set
A - a is ext-real set
- a is ext-real set
A + (- a) is ext-real set
B - a is ext-real set
B + (- a) is ext-real set
z is ext-real set
{a,z} is non empty ext-real-membered set
({A,B},{a,z}) is non empty ext-real-membered set
({a,z}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a,z} } is set
({A,B},({a,z})) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in ({a,z}) ) } is set
A - z is ext-real set
- z is ext-real set
A + (- z) is ext-real set
B - z is ext-real set
B + (- z) is ext-real set
{(A - a),(A - z),(B - a),(B - z)} is ext-real-membered set
{(- a),(- z)} is non empty ext-real-membered set
({A,B},{(- a),(- z)}) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in {(- a),(- z)} ) } is set
A is complex-membered set
B is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
{ (b₁ - b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
- c2 is complex Element of COMPLEX
z - (- c2) is complex Element of COMPLEX
- (- c2) is complex set
z + (- (- c2)) is complex set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z - c2 is complex Element of COMPLEX
- c2 is complex set
z + (- c2) is complex set
- c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex set
z is complex set
a - z is complex Element of COMPLEX
- z is complex set
a + (- z) is complex set
{ (b₁ - b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(B,A) is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
(B,(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (A) ) } is set
A is non empty complex-membered set
B is non empty complex-membered set
(A,B) is set
(B) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex-membered ext-real-membered real-membered set
(A,B) is complex-membered set
(B) is complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex-membered ext-real-membered real-membered rational-membered set
(A,B) is complex-membered ext-real-membered real-membered set
(B) is complex-membered ext-real-membered real-membered rational-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
B is complex-membered ext-real-membered real-membered rational-membered integer-membered set
(A,B) is complex-membered ext-real-membered real-membered rational-membered set
(B) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered ext-real-membered real-membered set
a is ext-real-membered set
B is complex-membered ext-real-membered real-membered set
z is ext-real-membered set
(A,B) is complex-membered ext-real-membered real-membered set
(B) is complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
(a,z) is ext-real-membered set
(z) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in z } is set
(a,(z)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in a & b₂ in (z) ) } is set
(A,B) is ext-real-membered set
(A,(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
a is complex-membered set
(A,a) is complex-membered set
(a) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
(A,(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
z is complex-membered set
(B,z) is complex-membered set
(z) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in z } is set
(B,(z)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (z) ) } is set
c2 is complex set
{ (b₁ - b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
w3 - c3 is complex Element of COMPLEX
- c3 is complex set
w3 + (- c3) is complex set
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
((A),(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A) & b₂ in (B) ) } is set
a is complex set
z is complex Element of COMPLEX
- z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
- c2 is complex Element of COMPLEX
- w3 is complex Element of COMPLEX
(- c2) + (- w3) is complex Element of COMPLEX
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
- z is complex Element of COMPLEX
- c2 is complex Element of COMPLEX
(- z) + (- c2) is complex Element of COMPLEX
- a is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
B \/ a is complex-membered set
(A,(B \/ a)) is complex-membered set
((B \/ a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B \/ a } is set
(A,((B \/ a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B \/ a)) ) } is set
(A,a) is complex-membered set
(a) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
(A,(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
(A,B) \/ (A,a) is complex-membered set
(B) \/ (a) is complex-membered set
(A,((B) \/ (a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) \/ (a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
B /\ a is complex-membered set
(A,(B /\ a)) is complex-membered set
((B /\ a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B /\ a } is set
(A,((B /\ a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B /\ a)) ) } is set
(A,a) is complex-membered set
(a) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
(A,(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
(A,B) /\ (A,a) is complex-membered set
(B) /\ (a) is complex-membered set
(A,((B) /\ (a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) /\ (a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
((A),B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
((A),(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A) & b₂ in (B) ) } is set
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
((A),B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A) & b₂ in B ) } is set
((A),(B)) is complex-membered set
((B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B) } is set
((A),((B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A) & b₂ in ((B)) ) } is set
A is complex-membered set
B is complex-membered set
a is complex-membered set
(B,a) is complex-membered set
(a) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
(B,(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (a) ) } is set
(A,(B,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B,a) ) } is set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
((A,B),a) is complex-membered set
((A,B),(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
(B,a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in a ) } is set
(A,(B,a)) is complex-membered set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
(A,((B,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B,a)) ) } is set
((A,B),a) is complex-membered set
(a) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
((A,B),(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (a) ) } is set
((B),a) is complex-membered set
((B),(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (B) & b₂ in (a) ) } is set
(A,((B),a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B),a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
(B,a) is complex-membered set
(a) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
(B,(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (a) ) } is set
(A,(B,a)) is complex-membered set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
(A,((B,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B,a)) ) } is set
((A,B),a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in a ) } is set
((B),a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (B) & b₂ in a ) } is set
(A,((B),a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B),a) ) } is set
A is complex set
{A} is non empty complex-membered set
B is complex set
{B} is non empty complex-membered set
({A},{B}) is non empty complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({A},({B})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in ({B}) ) } is set
A - B is complex Element of COMPLEX
- B is complex set
A + (- B) is complex set
{(A - B)} is non empty complex-membered set
- B is complex Element of COMPLEX
{(- B)} is non empty complex-membered set
({A},{(- B)}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {(- B)} ) } is set
A is complex set
{A} is non empty complex-membered set
B is complex set
A - B is complex Element of COMPLEX
- B is complex set
A + (- B) is complex set
a is complex set
{B,a} is non empty complex-membered set
({A},{B,a}) is non empty complex-membered set
({B,a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B,a} } is set
({A},({B,a})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in ({B,a}) ) } is set
A - a is complex Element of COMPLEX
- a is complex set
A + (- a) is complex set
{(A - B),(A - a)} is non empty complex-membered set
- B is complex Element of COMPLEX
- a is complex Element of COMPLEX
{(- B),(- a)} is non empty complex-membered set
({A},{(- B),(- a)}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {(- B),(- a)} ) } is set
A is complex set
B is complex set
{A,B} is non empty complex-membered set
a is complex set
{a} is non empty complex-membered set
({A,B},{a}) is non empty complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
({A,B},({a})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in ({a}) ) } is set
A - a is complex Element of COMPLEX
- a is complex set
A + (- a) is complex set
B - a is complex Element of COMPLEX
B + (- a) is complex set
{(A - a),(B - a)} is non empty complex-membered set
- a is complex Element of COMPLEX
{(- a)} is non empty complex-membered set
({A,B},{(- a)}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in {(- a)} ) } is set
A is complex set
B is complex set
{A,B} is non empty complex-membered set
a is complex set
A - a is complex Element of COMPLEX
- a is complex set
A + (- a) is complex set
B - a is complex Element of COMPLEX
B + (- a) is complex set
z is complex set
{a,z} is non empty complex-membered set
({A,B},{a,z}) is non empty complex-membered set
({a,z}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a,z} } is set
({A,B},({a,z})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in ({a,z}) ) } is set
A - z is complex Element of COMPLEX
- z is complex set
A + (- z) is complex set
B - z is complex Element of COMPLEX
B + (- z) is complex set
{(A - a),(A - z),(B - a),(B - z)} is complex-membered set
- a is complex Element of COMPLEX
- z is complex Element of COMPLEX
{(- a),(- z)} is non empty complex-membered set
({A,B},{(- a),(- z)}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in {(- a),(- z)} ) } is set
A is ext-real-membered set
B is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is set
z is ext-real-membered set
c2 is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in z & b₂ in c2 ) } is set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in c2 & b₂ in z ) } is set
w3 is set
c3 is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(c3,c2) is ext-real Element of ExtREAL
w3 is set
c3 is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(c3,c2) is ext-real Element of ExtREAL
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real-membered set
(A,B) is set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
the Element of (A,B) is Element of (A,B)
a is ext-real Element of ExtREAL
z is ext-real Element of ExtREAL
(a,z) is ext-real Element of ExtREAL
(B,A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real set
z is ext-real set
a * z is ext-real set
A is non empty ext-real-membered set
B is non empty ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
the ext-real Element of A is ext-real Element of A
the ext-real Element of B is ext-real Element of B
the ext-real Element of A * the ext-real Element of B is ext-real set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real-membered set
((A,B),a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A,B) & b₂ in a ) } is set
(B,a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in a ) } is set
(A,(B,a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B,a) ) } is set
z is ext-real set
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(c3,c2) is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
(c3,(c2,w3)) is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(c3,c2) is ext-real Element of ExtREAL
(c2,c3) is ext-real Element of ExtREAL
((c2,c3),c2) is ext-real Element of ExtREAL
A is ext-real-membered set
B is ext-real-membered set
a is ext-real-membered set
(A,a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
z is ext-real-membered set
(B,z) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in z ) } is set
c2 is ext-real set
w3 is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
(w3,c3) is ext-real Element of ExtREAL
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real-membered set
B \/ a is ext-real-membered set
(A,(B \/ a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B \/ a ) } is set
(A,a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
(A,B) \/ (A,a) is ext-real-membered set
z is ext-real set
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real-membered set
B /\ a is ext-real-membered set
(A,(B /\ a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B /\ a ) } is set
(A,a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
(A,B) /\ (A,a) is ext-real-membered set
z is ext-real set
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
A is ext-real-membered set
B is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
((A,B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,B) } is set
a is ext-real set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
(c2) is ext-real Element of ExtREAL
(z,(c2)) is ext-real Element of ExtREAL
((z,c2)) is ext-real Element of ExtREAL
((z,(c2))) is ext-real Element of ExtREAL
- a is ext-real set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
(c2) is ext-real Element of ExtREAL
(z,(c2)) is ext-real Element of ExtREAL
((z,c2)) is ext-real Element of ExtREAL
A is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
((A,B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,B) } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
((A),(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A) & b₂ in (B) ) } is set
a is ext-real set
z is ext-real Element of ExtREAL
(z) is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(c2,w3) is ext-real Element of ExtREAL
(c2) is ext-real Element of ExtREAL
(w3) is ext-real Element of ExtREAL
((c2),(w3)) is ext-real Element of ExtREAL
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(w3) is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
(c3) is ext-real Element of ExtREAL
(c3,w3) is ext-real Element of ExtREAL
((c3,w3)) is ext-real Element of ExtREAL
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
{B} is non empty ext-real-membered set
({A},{B}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B} ) } is set
A * B is ext-real set
{(A * B)} is non empty ext-real-membered set
a is ext-real set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
A * B is ext-real set
a is ext-real set
{B,a} is non empty ext-real-membered set
({A},{B,a}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B,a} ) } is set
A * a is ext-real set
{(A * B),(A * a)} is non empty ext-real-membered set
{B} is non empty ext-real-membered set
{a} is non empty ext-real-membered set
{B} \/ {a} is non empty ext-real-membered set
({A},({B} \/ {a})) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B} \/ {a} ) } is set
({A},{B}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {B} ) } is set
({A},{a}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {a} ) } is set
({A},{B}) \/ ({A},{a}) is non empty ext-real-membered set
{(A * B)} is non empty ext-real-membered set
{(A * B)} \/ ({A},{a}) is non empty ext-real-membered set
{(A * a)} is non empty ext-real-membered set
{(A * B)} \/ {(A * a)} is non empty ext-real-membered set
A is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
a is ext-real set
A * a is ext-real set
B * a is ext-real set
z is ext-real set
{a,z} is non empty ext-real-membered set
({A,B},{a,z}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in {a,z} ) } is set
A * z is ext-real set
B * z is ext-real set
{(A * a),(A * z),(B * a),(B * z)} is ext-real-membered set
{A} is non empty ext-real-membered set
{B} is non empty ext-real-membered set
{A} \/ {B} is non empty ext-real-membered set
(({A} \/ {B}),{a,z}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} \/ {B} & b₂ in {a,z} ) } is set
({A},{a,z}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {a,z} ) } is set
({B},{a,z}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in {a,z} ) } is set
({A},{a,z}) \/ ({B},{a,z}) is non empty ext-real-membered set
{(A * a),(A * z)} is non empty ext-real-membered set
{(A * a),(A * z)} \/ ({B},{a,z}) is non empty ext-real-membered set
{(B * a),(B * z)} is non empty ext-real-membered set
{(A * a),(A * z)} \/ {(B * a),(B * z)} is non empty ext-real-membered set
A is complex-membered set
B is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex-membered set
c2 is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in z & b₂ in c2 ) } is set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in c2 & b₂ in z ) } is set
w3 is set
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 * c2 is complex Element of COMPLEX
w3 is set
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 * c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex set
z is complex set
a * z is complex Element of COMPLEX
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex-membered set
(A,B) is set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
the Element of (A,B) is Element of (A,B)
a is complex Element of COMPLEX
z is complex Element of COMPLEX
a * z is complex Element of COMPLEX
(B,A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in A ) } is set
A is non empty complex-membered set
B is non empty complex-membered set
(A,B) is set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
the complex Element of A is complex Element of A
the complex Element of B is complex Element of B
the complex Element of A * the complex Element of B is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
B is complex-membered ext-real-membered real-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex-membered ext-real-membered real-membered rational-membered set
(A,B) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
B is complex-membered ext-real-membered real-membered rational-membered integer-membered set
(A,B) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
B is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
(A,B) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
A is complex-membered ext-real-membered real-membered set
a is ext-real-membered set
B is complex-membered ext-real-membered real-membered set
z is ext-real-membered set
(A,B) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
(a,z) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in a & b₂ in z ) } is set
c2 is ext-real set
w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
w3 * c3 is complex Element of COMPLEX
c2 is ext-real Element of ExtREAL
d2 is ext-real Element of ExtREAL
(c2,d2) is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
(w3,c3) is ext-real Element of ExtREAL
c2 is complex Element of COMPLEX
d2 is complex Element of COMPLEX
c2 * d2 is complex Element of COMPLEX
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
((A,B),a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in a ) } is set
(B,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in a ) } is set
(A,(B,a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B,a) ) } is set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 * c2 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
c3 * (c2 * w3) is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 * c2 is complex Element of COMPLEX
c2 * c3 is complex Element of COMPLEX
(c2 * c3) * c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
a is complex-membered set
(A,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
z is complex-membered set
(B,z) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in z ) } is set
c2 is complex set
w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
w3 * c3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
B \/ a is complex-membered set
(A,(B \/ a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B \/ a ) } is set
(A,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
(A,B) \/ (A,a) is complex-membered set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
B /\ a is complex-membered set
(A,(B /\ a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B /\ a ) } is set
(A,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
(A,B) /\ (A,a) is complex-membered set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
a is complex set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
- c2 is complex Element of COMPLEX
z * (- c2) is complex Element of COMPLEX
- (z * (- c2)) is complex Element of COMPLEX
- a is complex Element of COMPLEX
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
- c2 is complex Element of COMPLEX
z * (- c2) is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
(B,a) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in a ) } is set
(A,(B,a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B,a) ) } is set
(A,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
((A,B),(A,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (A,a) ) } is set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
c3 + c2 is complex Element of COMPLEX
c2 * c2 is complex Element of COMPLEX
c2 * c3 is complex Element of COMPLEX
(c2 * c3) + (c2 * c2) is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
(B,a) is complex-membered set
(a) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in a } is set
(B,(a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (a) ) } is set
(A,(B,a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B,a) ) } is set
(A,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
((A,B),(A,a)) is complex-membered set
((A,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) } is set
((A,B),((A,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in ((A,a)) ) } is set
(A,(B,(a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B,(a)) ) } is set
(A,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
((A,B),(A,(a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (A,(a)) ) } is set
A is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
((A,B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
((A),(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A) & b₂ in (B) ) } is set
a is complex set
z is complex Element of COMPLEX
z " is complex Element of COMPLEX
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 * w3 is complex Element of COMPLEX
c2 " is complex Element of COMPLEX
w3 " is complex Element of COMPLEX
(c2 ") * (w3 ") is complex Element of COMPLEX
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
w3 " is complex Element of COMPLEX
c3 is complex Element of COMPLEX
c3 " is complex Element of COMPLEX
c3 * w3 is complex Element of COMPLEX
(c3 * w3) " is complex Element of COMPLEX
A is complex set
{A} is non empty complex-membered set
B is complex set
{B} is non empty complex-membered set
({A},{B}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B} ) } is set
A * B is complex Element of COMPLEX
{(A * B)} is non empty complex-membered set
a is complex set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
A is complex set
{A} is non empty complex-membered set
B is complex set
A * B is complex Element of COMPLEX
a is complex set
{B,a} is non empty complex-membered set
({A},{B,a}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B,a} ) } is set
A * a is complex Element of COMPLEX
{(A * B),(A * a)} is non empty complex-membered set
{B} is non empty complex-membered set
{a} is non empty complex-membered set
{B} \/ {a} is non empty complex-membered set
({A},({B} \/ {a})) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B} \/ {a} ) } is set
({A},{B}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {B} ) } is set
({A},{a}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {a} ) } is set
({A},{B}) \/ ({A},{a}) is non empty complex-membered set
{(A * B)} is non empty complex-membered set
{(A * B)} \/ ({A},{a}) is non empty complex-membered set
{(A * a)} is non empty complex-membered set
{(A * B)} \/ {(A * a)} is non empty complex-membered set
A is complex set
B is complex set
{A,B} is non empty complex-membered set
a is complex set
A * a is complex Element of COMPLEX
B * a is complex Element of COMPLEX
z is complex set
{a,z} is non empty complex-membered set
({A,B},{a,z}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in {a,z} ) } is set
A * z is complex Element of COMPLEX
B * z is complex Element of COMPLEX
{(A * a),(A * z),(B * a),(B * z)} is complex-membered set
{A} is non empty complex-membered set
{B} is non empty complex-membered set
{A} \/ {B} is non empty complex-membered set
(({A} \/ {B}),{a,z}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} \/ {B} & b₂ in {a,z} ) } is set
({A},{a,z}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {a,z} ) } is set
({B},{a,z}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in {a,z} ) } is set
({A},{a,z}) \/ ({B},{a,z}) is non empty complex-membered set
{(A * a),(A * z)} is non empty complex-membered set
{(A * a),(A * z)} \/ ({B},{a,z}) is non empty complex-membered set
{(B * a),(B * z)} is non empty complex-membered set
{(A * a),(A * z)} \/ {(B * a),(B * z)} is non empty complex-membered set
A is ext-real-membered set
B is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
{ (b₁ / b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(w3) is ext-real Element of ExtREAL
z / w3 is ext-real set
w3 " is ext-real set
z * (w3 ") is ext-real set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z / c2 is ext-real set
c2 " is ext-real set
z * (c2 ") is ext-real set
(c2) is ext-real Element of ExtREAL
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real set
z is ext-real set
a / z is ext-real set
z " is ext-real set
a * (z ") is ext-real set
{ (b₁ / b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
(B,A) is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
(B,(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in (A) ) } is set
A is non empty ext-real-membered set
B is non empty ext-real-membered set
(A,B) is set
(B) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
a is ext-real-membered set
(A,a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
(A,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
z is ext-real-membered set
(B,z) is ext-real-membered set
(z) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in z } is set
(B,(z)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in (z) ) } is set
c2 is ext-real set
{ (b₁ / b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
w3 is ext-real Element of ExtREAL
c3 is ext-real Element of ExtREAL
w3 / c3 is ext-real set
c3 " is ext-real set
w3 * (c3 ") is ext-real set
A is ext-real-membered set
B is ext-real-membered set
A \/ B is ext-real-membered set
a is ext-real-membered set
((A \/ B),a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
((A \/ B),(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A \/ B & b₂ in (a) ) } is set
(A,a) is ext-real-membered set
(A,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
(B,a) is ext-real-membered set
(B,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in (a) ) } is set
(A,a) \/ (B,a) is ext-real-membered set
A is ext-real-membered set
B is ext-real-membered set
A /\ B is ext-real-membered set
a is ext-real-membered set
((A /\ B),a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
((A /\ B),(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A /\ B & b₂ in (a) ) } is set
(A,a) is ext-real-membered set
(A,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
(B,a) is ext-real-membered set
(B,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in (a) ) } is set
(A,a) /\ (B,a) is ext-real-membered set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real-membered set
B \/ a is ext-real-membered set
(A,(B \/ a)) is ext-real-membered set
((B \/ a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B \/ a } is set
(A,((B \/ a))) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ((B \/ a)) ) } is set
(A,a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
(A,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
(A,B) \/ (A,a) is ext-real-membered set
(B) \/ (a) is ext-real-membered set
(A,((B) \/ (a))) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) \/ (a) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real-membered set
B /\ a is ext-real-membered set
(A,(B /\ a)) is ext-real-membered set
((B /\ a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B /\ a } is set
(A,((B /\ a))) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ((B /\ a)) ) } is set
(A,a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
(A,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (a) ) } is set
(A,B) /\ (A,a) is ext-real-membered set
(B) /\ (a) is ext-real-membered set
(A,((B) /\ (a))) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) /\ (a) ) } is set
(A,(B)) /\ (A,(a)) is ext-real-membered set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in B ) } is set
a is ext-real-membered set
((A,B),a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
((A,B),(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A,B) & b₂ in (a) ) } is set
(B,a) is ext-real-membered set
(B,(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in (a) ) } is set
(A,(B,a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B,a) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real-membered set
((A,B),a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A,B) & b₂ in a ) } is set
(A,a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in a ) } is set
((A,a),B) is ext-real-membered set
((A,a),(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A,a) & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
(A,B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
a is ext-real-membered set
((A,B),a) is ext-real-membered set
(a) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in a } is set
((A,B),(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (A,B) & b₂ in (a) ) } is set
(B,a) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in a ) } is set
(A,(B,a)) is ext-real-membered set
((B,a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (B,a) } is set
(A,((B,a))) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ((B,a)) ) } is set
((B),(a)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in (B) & b₂ in (a) ) } is set
(A,((B),(a))) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ((B),(a)) ) } is set
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
{B} is non empty ext-real-membered set
({A},{B}) is non empty ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
({A},({B})) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in ({B}) ) } is set
A / B is ext-real set
B " is ext-real set
A * (B ") is ext-real set
{(A / B)} is non empty ext-real-membered set
{(B ")} is non empty ext-real-membered set
({A},{(B ")}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {(B ")} ) } is set
A is ext-real set
{A} is non empty ext-real-membered set
B is ext-real set
A / B is ext-real set
B " is ext-real set
A * (B ") is ext-real set
a is ext-real set
{B,a} is non empty ext-real-membered set
({A},{B,a}) is non empty ext-real-membered set
({B,a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B,a} } is set
({A},({B,a})) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in ({B,a}) ) } is set
A / a is ext-real set
a " is ext-real set
A * (a ") is ext-real set
{(A / B),(A / a)} is non empty ext-real-membered set
{(B "),(a ")} is non empty ext-real-membered set
({A},{(B "),(a ")}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A} & b₂ in {(B "),(a ")} ) } is set
A is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
a is ext-real set
{a} is non empty ext-real-membered set
({A,B},{a}) is non empty ext-real-membered set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
({A,B},({a})) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in ({a}) ) } is set
A / a is ext-real set
a " is ext-real set
A * (a ") is ext-real set
B / a is ext-real set
B * (a ") is ext-real set
{(A / a),(B / a)} is non empty ext-real-membered set
{(a ")} is non empty ext-real-membered set
({A,B},{(a ")}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in {(a ")} ) } is set
A is ext-real set
B is ext-real set
{A,B} is non empty ext-real-membered set
a is ext-real set
A / a is ext-real set
a " is ext-real set
A * (a ") is ext-real set
B / a is ext-real set
B * (a ") is ext-real set
z is ext-real set
{a,z} is non empty ext-real-membered set
({A,B},{a,z}) is non empty ext-real-membered set
({a,z}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a,z} } is set
({A,B},({a,z})) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in ({a,z}) ) } is set
A / z is ext-real set
z " is ext-real set
A * (z ") is ext-real set
B / z is ext-real set
B * (z ") is ext-real set
{(A / a),(A / z),(B / a),(B / z)} is ext-real-membered set
{(a "),(z ")} is non empty ext-real-membered set
({A,B},{(a "),(z ")}) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {A,B} & b₂ in {(a "),(z ")} ) } is set
A is complex-membered set
B is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
{ (b₁ / b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
c2 " is complex Element of COMPLEX
z / (c2 ") is complex Element of COMPLEX
(c2 ") " is complex set
z * ((c2 ") ") is complex set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z / c2 is complex Element of COMPLEX
c2 " is complex set
z * (c2 ") is complex set
c2 " is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex set
z is complex set
a / z is complex Element of COMPLEX
z " is complex set
a * (z ") is complex set
{ (b₁ / b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(B,A) is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
(B,(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (A) ) } is set
A is non empty complex-membered set
B is non empty complex-membered set
(A,B) is set
(B) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex-membered ext-real-membered real-membered set
(A,B) is complex-membered set
(B) is complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex-membered ext-real-membered real-membered rational-membered set
(A,B) is complex-membered ext-real-membered real-membered set
(B) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered ext-real-membered real-membered set
a is ext-real-membered set
B is complex-membered ext-real-membered real-membered set
z is ext-real-membered set
(A,B) is complex-membered ext-real-membered real-membered set
(B) is complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
(A,(B)) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
(a,z) is ext-real-membered set
(z) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in z } is set
(a,(z)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in a & b₂ in (z) ) } is set
(A,B) is ext-real-membered set
(A,(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
a is complex-membered set
(A,a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
(A,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
z is complex-membered set
(B,z) is complex-membered set
(z) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in z } is set
(B,(z)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (z) ) } is set
c2 is complex set
{ (b₁ / b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
w3 / c3 is complex Element of COMPLEX
c3 " is complex set
w3 * (c3 ") is complex set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
B \/ a is complex-membered set
(A,(B \/ a)) is complex-membered set
((B \/ a)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B \/ a } is set
(A,((B \/ a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B \/ a)) ) } is set
(A,a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
(A,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
(A,B) \/ (A,a) is complex-membered set
(B) \/ (a) is complex-membered set
(A,((B) \/ (a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) \/ (a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
B /\ a is complex-membered set
(A,(B /\ a)) is complex-membered set
((B /\ a)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B /\ a } is set
(A,((B /\ a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B /\ a)) ) } is set
(A,a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
(A,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
(A,B) /\ (A,a) is complex-membered set
(B) /\ (a) is complex-membered set
(A,((B) /\ (a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) /\ (a) ) } is set
A is complex-membered set
B is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
((B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (B) } is set
(A,((B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B)) ) } is set
(A,B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
((B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B) } is set
(A,((B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B)) ) } is set
A is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
B is complex-membered set
((A),B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
((A),(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A) & b₂ in (B) ) } is set
(A,B) is complex-membered set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
((A,B),a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
((A,B),(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (a) ) } is set
(A,a) is complex-membered set
(A,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
(B,a) is complex-membered set
(B,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (a) ) } is set
((A,a),(B,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in (B,a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
((A,B),a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
((A,B),(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (a) ) } is set
(A,a) is complex-membered set
(A,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (a) ) } is set
(B,a) is complex-membered set
(B,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (a) ) } is set
((A,a),(B,a)) is complex-membered set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
((A,a),((B,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in ((B,a)) ) } is set
((A,(B)),a) is complex-membered set
((A,(B)),(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,(B)) & b₂ in (a) ) } is set
((B),a) is complex-membered set
((B),(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (B) & b₂ in (a) ) } is set
((A,a),((B),a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in ((B),a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex-membered set
((A,B),a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
((A,B),(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (a) ) } is set
(B,a) is complex-membered set
(B,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (a) ) } is set
(A,(B,a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B,a) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
((A,B),a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in a ) } is set
(A,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
((A,a),B) is complex-membered set
((A,a),(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex-membered set
((A,B),a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
((A,B),(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (a) ) } is set
(B,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in a ) } is set
(A,(B,a)) is complex-membered set
((B,a)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
(A,((B,a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B,a)) ) } is set
((B),(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (B) & b₂ in (a) ) } is set
(A,((B),(a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B),(a)) ) } is set
A is complex-membered set
B is complex-membered set
a is complex-membered set
(B,a) is complex-membered set
(a) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in a } is set
(B,(a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in (a) ) } is set
(A,(B,a)) is complex-membered set
((B,a)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
(A,((B,a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B,a)) ) } is set
(A,a) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in a ) } is set
((A,a),B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
((A,a),(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in (B) ) } is set
((a)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in (a) } is set
((B),((a))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (B) & b₂ in ((a)) ) } is set
(A,((B),((a)))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ((B),((a))) ) } is set
A is complex set
{A} is non empty complex-membered set
B is complex set
{B} is non empty complex-membered set
({A},{B}) is non empty complex-membered set
({B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({A},({B})) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in ({B}) ) } is set
A / B is complex Element of COMPLEX
B " is complex set
A * (B ") is complex set
{(A / B)} is non empty complex-membered set
B " is complex Element of COMPLEX
{(B ")} is non empty complex-membered set
({A},{(B ")}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {(B ")} ) } is set
A is complex set
{A} is non empty complex-membered set
B is complex set
A / B is complex Element of COMPLEX
B " is complex set
A * (B ") is complex set
a is complex set
{B,a} is non empty complex-membered set
({A},{B,a}) is non empty complex-membered set
({B,a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B,a} } is set
({A},({B,a})) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in ({B,a}) ) } is set
A / a is complex Element of COMPLEX
a " is complex set
A * (a ") is complex set
{(A / B),(A / a)} is non empty complex-membered set
B " is complex Element of COMPLEX
a " is complex Element of COMPLEX
{(B "),(a ")} is non empty complex-membered set
({A},{(B "),(a ")}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A} & b₂ in {(B "),(a ")} ) } is set
A is complex set
B is complex set
{A,B} is non empty complex-membered set
a is complex set
{a} is non empty complex-membered set
({A,B},{a}) is non empty complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
({A,B},({a})) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in ({a}) ) } is set
A / a is complex Element of COMPLEX
a " is complex set
A * (a ") is complex set
B / a is complex Element of COMPLEX
B * (a ") is complex set
{(A / a),(B / a)} is non empty complex-membered set
a " is complex Element of COMPLEX
{(a ")} is non empty complex-membered set
({A,B},{(a ")}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in {(a ")} ) } is set
A is complex set
B is complex set
{A,B} is non empty complex-membered set
a is complex set
A / a is complex Element of COMPLEX
a " is complex set
A * (a ") is complex set
B / a is complex Element of COMPLEX
B * (a ") is complex set
z is complex set
{a,z} is non empty complex-membered set
({A,B},{a,z}) is non empty complex-membered set
({a,z}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a,z} } is set
({A,B},({a,z})) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in ({a,z}) ) } is set
A / z is complex Element of COMPLEX
z " is complex set
A * (z ") is complex set
B / z is complex Element of COMPLEX
B * (z ") is complex set
{(A / a),(A / z),(B / a),(B / z)} is complex-membered set
a " is complex Element of COMPLEX
z " is complex Element of COMPLEX
{(a "),(z ")} is non empty complex-membered set
({A,B},{(a "),(z ")}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {A,B} & b₂ in {(a "),(z ")} ) } is set
B is ext-real set
{B} is non empty ext-real-membered set
A is ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real set
a is ext-real set
a + B is ext-real set
(A,a) is set
{a} is non empty ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
{ (B + b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z + c2 is ext-real set
a is set
z is ext-real Element of ExtREAL
B + z is ext-real set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
a is set
{ (B + b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is non empty ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real-membered set
a is complex real ext-real set
(A,a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
z is ext-real set
a + z is ext-real set
c2 is ext-real Element of ExtREAL
a + c2 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
a is complex real ext-real set
(A,a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
A is ext-real-membered set
B is ext-real-membered set
A /\ B is ext-real-membered set
a is complex real ext-real set
((A /\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A /\ B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A /\ B ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) /\ (B,a) is ext-real-membered set
z is ext-real set
c2 is ext-real Element of ExtREAL
a + c2 is ext-real set
w3 is ext-real Element of ExtREAL
a + w3 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
a is ext-real set
(A,a) is ext-real-membered set
{a} is non empty ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
((A \ B),a) is ext-real-membered set
({a},(A \ B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \ B ) } is set
z is ext-real set
c2 is ext-real Element of ExtREAL
a + c2 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
a is complex real ext-real set
((A \ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A \ B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \ B ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
z is ext-real set
c2 is ext-real Element of ExtREAL
a + c2 is ext-real set
w3 is ext-real Element of ExtREAL
a + w3 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
A \+\ B is ext-real-membered set
A \ B is ext-real-membered set
B \ A is ext-real-membered set
(A \ B) \/ (B \ A) is ext-real-membered set
a is complex real ext-real set
((A \+\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A \+\ B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \+\ B ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \+\ (B,a) is ext-real-membered set
(A,a) \ (B,a) is ext-real-membered set
(B,a) \ (A,a) is ext-real-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
((A \ B),a) is ext-real-membered set
({a},(A \ B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \ B ) } is set
B \ A is ext-real-membered Element of K13(B)
K13(B) is set
((B \ A),a) is ext-real-membered set
({a},(B \ A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B \ A ) } is set
((A \ B),a) \/ ((B \ A),a) is ext-real-membered set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
((A,a) \ (B,a)) \/ ((B \ A),a) is ext-real-membered set
B is complex set
{B} is non empty complex-membered set
A is complex-membered set
({B},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered set
B is complex set
a is complex set
a + B is complex Element of COMPLEX
(A,a) is set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
{ (B + b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z + c2 is complex Element of COMPLEX
a is set
z is complex Element of COMPLEX
B + z is complex Element of COMPLEX
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
a is set
{ (B + b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is non empty complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex real ext-real set
(A,B) is complex-membered set
{B} is non empty complex-membered ext-real-membered real-membered set
({B},A) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex real rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
B is complex real integer rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered rational-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
B is complex epsilon-transitive epsilon-connected ordinal natural real integer rational ext-real non negative set
(A,B) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
a is complex real ext-real set
z is ext-real set
(A,a) is complex-membered ext-real-membered real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
({a},A) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,z) is ext-real-membered set
{z} is non empty ext-real-membered set
({z},B) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {z} & b₂ in B ) } is set
(A,a) is ext-real-membered set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
z is complex set
a + z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
a + c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
A is complex-membered set
(A,0) is complex-membered set
{0} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
({0},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {0} & b₂ in A ) } is set
B is complex set
a is complex Element of COMPLEX
z is complex Element of COMPLEX
a + z is complex Element of COMPLEX
0 + B is complex Element of COMPLEX
{ (0 + b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex-membered set
B is complex set
a is complex set
B + a is complex Element of COMPLEX
(A,(B + a)) is complex-membered set
{(B + a)} is non empty complex-membered set
({(B + a)},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(B + a)} & b₂ in A ) } is set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
((A,a),B) is complex-membered set
{B} is non empty complex-membered set
({B},(A,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A,a) ) } is set
({B},{a}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in {a} ) } is set
(({B},{a}),A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in ({B},{a}) & b₂ in A ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex set
((A,B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A,B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A,B) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
((A,a),B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in B ) } is set
A is complex-membered set
B is complex-membered set
A /\ B is complex-membered set
a is complex set
((A /\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A /\ B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A /\ B ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
(A,a) /\ (B,a) is complex-membered set
z is complex set
c2 is complex Element of COMPLEX
a + c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
a + w3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
a is complex set
((A \ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \ B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A \ B ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
z is complex set
c2 is complex Element of COMPLEX
a + c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
a + w3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
a + c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
a is complex set
((A \+\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \+\ B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A \+\ B ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \+\ (B,a) is complex-membered set
(A,a) \ (B,a) is complex-membered set
(B,a) \ (A,a) is complex-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
((A \ B),a) is complex-membered set
({a},(A \ B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A \ B ) } is set
B \ A is complex-membered Element of K13(B)
K13(B) is set
((B \ A),a) is complex-membered set
({a},(B \ A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B \ A ) } is set
((A \ B),a) \/ ((B \ A),a) is complex-membered set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
((A,a) \ (B,a)) \/ ((B \ A),a) is complex-membered set
B is ext-real set
{B} is non empty ext-real-membered set
A is ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
A is ext-real-membered set
B is ext-real set
a is ext-real set
a - B is ext-real set
- B is ext-real set
a + (- B) is ext-real set
(A,a) is set
{a} is non empty ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
{ (B - b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z + c2 is ext-real set
(c2) is ext-real Element of ExtREAL
z - (c2) is ext-real set
- (c2) is ext-real set
z + (- (c2)) is ext-real set
a is set
z is ext-real Element of ExtREAL
B - z is ext-real set
- z is ext-real set
B + (- z) is ext-real set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
a is set
{ (B - b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
A is non empty ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is non empty ext-real-membered set
(A) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
A is ext-real-membered set
B is ext-real-membered set
a is complex real ext-real set
(A,a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
z is ext-real set
a - z is ext-real set
- z is ext-real set
a + (- z) is ext-real set
c2 is ext-real Element of ExtREAL
a - c2 is ext-real set
- c2 is ext-real set
a + (- c2) is ext-real set
A is ext-real-membered set
B is ext-real-membered set
a is complex real ext-real set
(A,a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
A is ext-real-membered set
B is ext-real-membered set
A /\ B is ext-real-membered set
a is complex real ext-real set
((A /\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A /\ B)) is ext-real-membered set
((A /\ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A /\ B } is set
({a},((A /\ B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in ((A /\ B)) ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) /\ (B,a) is ext-real-membered set
(A) /\ (B) is ext-real-membered set
(((A) /\ (B)),a) is ext-real-membered set
({a},((A) /\ (B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) /\ (B) ) } is set
((A),a) is ext-real-membered set
((B),a) is ext-real-membered set
((A),a) /\ ((B),a) is ext-real-membered set
A is ext-real-membered set
B is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
a is complex real ext-real set
((A \ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A \ B)) is ext-real-membered set
((A \ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \ B } is set
({a},((A \ B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in ((A \ B)) ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
(A) \ (B) is ext-real-membered Element of K13((A))
K13((A)) is set
(((A) \ (B)),a) is ext-real-membered set
({a},((A) \ (B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) \ (B) ) } is set
((A),a) is ext-real-membered set
((B),a) is ext-real-membered set
((A),a) \ ((B),a) is ext-real-membered Element of K13(((A),a))
K13(((A),a)) is set
A is ext-real-membered set
B is ext-real-membered set
A \+\ B is ext-real-membered set
A \ B is ext-real-membered set
B \ A is ext-real-membered set
(A \ B) \/ (B \ A) is ext-real-membered set
a is complex real ext-real set
((A \+\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A \+\ B)) is ext-real-membered set
((A \+\ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \+\ B } is set
({a},((A \+\ B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in ((A \+\ B)) ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \+\ (B,a) is ext-real-membered set
(A,a) \ (B,a) is ext-real-membered set
(B,a) \ (A,a) is ext-real-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is ext-real-membered set
(A) \+\ (B) is ext-real-membered set
(A) \ (B) is ext-real-membered set
(B) \ (A) is ext-real-membered set
((A) \ (B)) \/ ((B) \ (A)) is ext-real-membered set
(((A) \+\ (B)),a) is ext-real-membered set
({a},((A) \+\ (B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) \+\ (B) ) } is set
((A),a) is ext-real-membered set
((B),a) is ext-real-membered set
((A),a) \+\ ((B),a) is ext-real-membered set
((A),a) \ ((B),a) is ext-real-membered set
((B),a) \ ((A),a) is ext-real-membered set
(((A),a) \ ((B),a)) \/ (((B),a) \ ((A),a)) is ext-real-membered set
B is complex set
{B} is non empty complex-membered set
A is complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is complex-membered set
B is complex set
a is complex set
a - B is complex Element of COMPLEX
- B is complex set
a + (- B) is complex set
(A,a) is set
{a} is non empty complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
{ (B - b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
{ (b₁ - b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z - c2 is complex Element of COMPLEX
- c2 is complex set
z + (- c2) is complex set
a is set
z is complex Element of COMPLEX
B - z is complex Element of COMPLEX
- z is complex set
B + (- z) is complex set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
a is set
{ (B - b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is non empty complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is non empty complex-membered set
(A) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex real ext-real set
(A,B) is complex-membered set
{B} is non empty complex-membered ext-real-membered real-membered set
({B},A) is complex-membered ext-real-membered real-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
({B},(A)) is ext-real-membered set
({B},A) is ext-real-membered set
({B},(A)) is ext-real-membered set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex real rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered set
(A) is complex-membered ext-real-membered real-membered rational-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
({B},(A)) is ext-real-membered set
({B},A) is ext-real-membered set
({B},(A)) is ext-real-membered set
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
B is complex real integer rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered rational-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
(A) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
({B},(A)) is ext-real-membered set
({B},A) is ext-real-membered set
({B},(A)) is ext-real-membered set
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
a is complex real ext-real set
z is ext-real set
(A,a) is complex-membered ext-real-membered real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is complex-membered ext-real-membered real-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
({a},(A)) is ext-real-membered set
({a},A) is ext-real-membered set
({a},(A)) is ext-real-membered set
(B,z) is ext-real-membered set
{z} is non empty ext-real-membered set
({z},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({z},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {z} & b₂ in (B) ) } is set
(A,a) is ext-real-membered set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
z is complex set
a - z is complex Element of COMPLEX
- z is complex set
a + (- z) is complex set
c2 is complex Element of COMPLEX
a - c2 is complex Element of COMPLEX
- c2 is complex set
a + (- c2) is complex set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
A /\ B is complex-membered set
a is complex set
((A /\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A /\ B)) is complex-membered set
((A /\ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A /\ B } is set
({a},((A /\ B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A /\ B)) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) /\ (B,a) is complex-membered set
(A) /\ (B) is complex-membered set
(((A) /\ (B)),a) is complex-membered set
({a},((A) /\ (B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) /\ (B) ) } is set
((A),a) is complex-membered set
((B),a) is complex-membered set
((A),a) /\ ((B),a) is complex-membered set
A is complex-membered set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
a is complex set
((A \ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \ B)) is complex-membered set
((A \ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \ B } is set
({a},((A \ B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A \ B)) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
(A) \ (B) is complex-membered Element of K13((A))
K13((A)) is set
(((A) \ (B)),a) is complex-membered set
({a},((A) \ (B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) \ (B) ) } is set
((A),a) is complex-membered set
((B),a) is complex-membered set
((A),a) \ ((B),a) is complex-membered Element of K13(((A),a))
K13(((A),a)) is set
A is complex-membered set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
a is complex set
((A \+\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \+\ B)) is complex-membered set
((A \+\ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \+\ B } is set
({a},((A \+\ B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A \+\ B)) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \+\ (B,a) is complex-membered set
(A,a) \ (B,a) is complex-membered set
(B,a) \ (A,a) is complex-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is complex-membered set
(A) \+\ (B) is complex-membered set
(A) \ (B) is complex-membered set
(B) \ (A) is complex-membered set
((A) \ (B)) \/ ((B) \ (A)) is complex-membered set
(((A) \+\ (B)),a) is complex-membered set
({a},((A) \+\ (B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) \+\ (B) ) } is set
((A),a) is complex-membered set
((B),a) is complex-membered set
((A),a) \+\ ((B),a) is complex-membered set
((A),a) \ ((B),a) is complex-membered set
((B),a) \ ((A),a) is complex-membered set
(((A),a) \ ((B),a)) \/ (((B),a) \ ((A),a)) is complex-membered set
A is ext-real-membered set
B is ext-real set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is ext-real-membered set
B is ext-real set
a is ext-real set
B - a is ext-real set
- a is ext-real set
B + (- a) is ext-real set
(A,a) is set
{a} is non empty ext-real-membered set
(A,{a}) is ext-real-membered set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
(A,({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({a}) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
{ (b₁ - B) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
z + c2 is ext-real set
(c2) is ext-real Element of ExtREAL
z - (c2) is ext-real set
- (c2) is ext-real set
z + (- (c2)) is ext-real set
a is set
z is ext-real Element of ExtREAL
z - B is ext-real set
- B is ext-real set
z + (- B) is ext-real set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
a is set
{ (b₁ - B) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is non empty ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is non empty ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is non empty ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is ext-real-membered set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
(A,B) is ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
((A,B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,B) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is ext-real-membered set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
(A,B) is ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
((A,B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,B) } is set
A is ext-real-membered set
B is ext-real-membered set
A /\ B is ext-real-membered set
a is complex real ext-real set
((A /\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
((A /\ B),{a}) is ext-real-membered set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
((A /\ B),({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A /\ B & b₂ in ({a}) ) } is set
(A,a) is ext-real-membered set
(A,{a}) is ext-real-membered set
(A,({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is ext-real-membered set
(B,{a}) is ext-real-membered set
(B,({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) /\ (B,a) is ext-real-membered set
((A /\ B),a) is ext-real-membered set
({a},(A /\ B)) is ext-real-membered set
((A /\ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A /\ B } is set
({a},((A /\ B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in ((A /\ B)) ) } is set
(((A /\ B),a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in ((A /\ B),a) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) /\ (B,a) is ext-real-membered set
(((A,a) /\ (B,a))) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,a) /\ (B,a) } is set
((A,a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,a) } is set
((B,a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (B,a) } is set
((A,a)) /\ ((B,a)) is ext-real-membered set
((A,a)) /\ (B,a) is ext-real-membered set
A is ext-real-membered set
B is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
a is complex real ext-real set
((A \ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
((A \ B),{a}) is ext-real-membered set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
((A \ B),({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A \ B & b₂ in ({a}) ) } is set
(A,a) is ext-real-membered set
(A,{a}) is ext-real-membered set
(A,({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is ext-real-membered set
(B,{a}) is ext-real-membered set
(B,({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
((A \ B),a) is ext-real-membered set
({a},(A \ B)) is ext-real-membered set
((A \ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \ B } is set
({a},((A \ B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in ((A \ B)) ) } is set
(((A \ B),a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in ((A \ B),a) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
(((A,a) \ (B,a))) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,a) \ (B,a) } is set
((A,a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,a) } is set
((B,a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (B,a) } is set
((A,a)) \ ((B,a)) is ext-real-membered Element of K13(((A,a)))
K13(((A,a))) is set
((A,a)) \ (B,a) is ext-real-membered Element of K13(((A,a)))
A is ext-real-membered set
B is ext-real-membered set
A \+\ B is ext-real-membered set
A \ B is ext-real-membered set
B \ A is ext-real-membered set
(A \ B) \/ (B \ A) is ext-real-membered set
a is complex real ext-real set
((A \+\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
((A \+\ B),{a}) is ext-real-membered set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
((A \+\ B),({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A \+\ B & b₂ in ({a}) ) } is set
(A,a) is ext-real-membered set
(A,{a}) is ext-real-membered set
(A,({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is ext-real-membered set
(B,{a}) is ext-real-membered set
(B,({a})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) \+\ (B,a) is ext-real-membered set
(A,a) \ (B,a) is ext-real-membered set
(B,a) \ (A,a) is ext-real-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is ext-real-membered set
((A \+\ B),a) is ext-real-membered set
({a},(A \+\ B)) is ext-real-membered set
((A \+\ B)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A \+\ B } is set
({a},((A \+\ B))) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in ((A \+\ B)) ) } is set
(((A \+\ B),a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in ((A \+\ B),a) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({a},(B)) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \+\ (B,a) is ext-real-membered set
(A,a) \ (B,a) is ext-real-membered set
(B,a) \ (A,a) is ext-real-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is ext-real-membered set
(((A,a) \+\ (B,a))) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,a) \+\ (B,a) } is set
((A,a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (A,a) } is set
((B,a)) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in (B,a) } is set
((A,a)) \+\ ((B,a)) is ext-real-membered set
((A,a)) \ ((B,a)) is ext-real-membered set
((B,a)) \ ((A,a)) is ext-real-membered set
(((A,a)) \ ((B,a))) \/ (((B,a)) \ ((A,a))) is ext-real-membered set
((A,a)) \+\ (B,a) is ext-real-membered set
((A,a)) \ (B,a) is ext-real-membered set
(B,a) \ ((A,a)) is ext-real-membered set
(((A,a)) \ (B,a)) \/ ((B,a) \ ((A,a))) is ext-real-membered set
A is complex-membered set
B is complex set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is complex-membered set
B is complex set
a is complex set
B - a is complex Element of COMPLEX
- a is complex set
B + (- a) is complex set
(A,a) is set
{a} is non empty complex-membered set
(A,{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
(A,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
{ (b₁ - B) where b₁ is complex Element of COMPLEX : b₁ in A } is set
{ (b₁ - b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in {B} ) } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z - c2 is complex Element of COMPLEX
- c2 is complex set
z + (- c2) is complex set
a is set
z is complex Element of COMPLEX
z - B is complex Element of COMPLEX
- B is complex set
z + (- B) is complex set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
a is set
{ (b₁ - B) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is non empty complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is non empty complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex real ext-real set
(A,B) is complex-membered set
{B} is non empty complex-membered ext-real-membered real-membered set
(A,{B}) is complex-membered ext-real-membered real-membered set
({B}) is non empty complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
(A,({B})) is ext-real-membered set
(A,{B}) is ext-real-membered set
(A,({B})) is ext-real-membered set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex real rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered set
(A,{B}) is complex-membered ext-real-membered real-membered rational-membered set
({B}) is non empty complex-membered ext-real-membered real-membered rational-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
(A,({B})) is ext-real-membered set
(A,{B}) is ext-real-membered set
(A,({B})) is ext-real-membered set
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
B is complex real integer rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered rational-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered set
(A,{B}) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
({B}) is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
(A,({B})) is ext-real-membered set
(A,{B}) is ext-real-membered set
(A,({B})) is ext-real-membered set
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
a is complex real ext-real set
z is ext-real set
(A,a) is complex-membered ext-real-membered real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
(A,{a}) is complex-membered ext-real-membered real-membered set
({a}) is non empty complex-membered ext-real-membered real-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
(A,({a})) is complex-membered ext-real-membered real-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(A,({a})) is ext-real-membered set
(A,{a}) is ext-real-membered set
(A,({a})) is ext-real-membered set
(B,z) is ext-real-membered set
{z} is non empty ext-real-membered set
(B,{z}) is ext-real-membered set
({z}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {z} } is set
(B,({z})) is ext-real-membered set
{ (b₁ + b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in ({z}) ) } is set
(A,a) is ext-real-membered set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
(A,{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
(A,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
z is complex set
z - a is complex Element of COMPLEX
- a is complex set
z + (- a) is complex set
c2 is complex Element of COMPLEX
c2 - a is complex Element of COMPLEX
c2 + (- a) is complex set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
(A,{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
(A,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
A is complex-membered set
B is complex set
(A,B) is complex-membered set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
(A,B) is complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
A is complex-membered set
B is complex set
(A,B) is complex-membered set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
(A,B) is complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
((A,B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,B) } is set
A is complex-membered set
B is complex-membered set
A /\ B is complex-membered set
a is complex set
((A /\ B),a) is complex-membered set
{a} is non empty complex-membered set
((A /\ B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A /\ B),({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A /\ B & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) /\ (B,a) is complex-membered set
((A /\ B),a) is complex-membered set
({a},(A /\ B)) is complex-membered set
((A /\ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A /\ B } is set
({a},((A /\ B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A /\ B)) ) } is set
(((A /\ B),a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in ((A /\ B),a) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) /\ (B,a) is complex-membered set
(((A,a) /\ (B,a))) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) /\ (B,a) } is set
((A,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) } is set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
((A,a)) /\ ((B,a)) is complex-membered set
((A,a)) /\ (B,a) is complex-membered set
A is complex-membered set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
a is complex set
((A \ B),a) is complex-membered set
{a} is non empty complex-membered set
((A \ B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A \ B),({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A \ B & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
((A \ B),a) is complex-membered set
({a},(A \ B)) is complex-membered set
((A \ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \ B } is set
({a},((A \ B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A \ B)) ) } is set
(((A \ B),a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in ((A \ B),a) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
(((A,a) \ (B,a))) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) \ (B,a) } is set
((A,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) } is set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
((A,a)) \ ((B,a)) is complex-membered Element of K13(((A,a)))
K13(((A,a))) is set
((A,a)) \ (B,a) is complex-membered Element of K13(((A,a)))
A is complex-membered set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
a is complex set
((A \+\ B),a) is complex-membered set
{a} is non empty complex-membered set
((A \+\ B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A \+\ B),({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A \+\ B & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) \+\ (B,a) is complex-membered set
(A,a) \ (B,a) is complex-membered set
(B,a) \ (A,a) is complex-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is complex-membered set
((A \+\ B),a) is complex-membered set
({a},(A \+\ B)) is complex-membered set
((A \+\ B)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A \+\ B } is set
({a},((A \+\ B))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A \+\ B)) ) } is set
(((A \+\ B),a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in ((A \+\ B),a) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \+\ (B,a) is complex-membered set
(A,a) \ (B,a) is complex-membered set
(B,a) \ (A,a) is complex-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is complex-membered set
(((A,a) \+\ (B,a))) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) \+\ (B,a) } is set
((A,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) } is set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
((A,a)) \+\ ((B,a)) is complex-membered set
((A,a)) \ ((B,a)) is complex-membered set
((B,a)) \ ((A,a)) is complex-membered set
(((A,a)) \ ((B,a))) \/ (((B,a)) \ ((A,a))) is complex-membered set
((A,a)) \+\ (B,a) is complex-membered set
((A,a)) \ (B,a) is complex-membered set
(B,a) \ ((A,a)) is complex-membered set
(((A,a)) \ (B,a)) \/ ((B,a) \ ((A,a))) is complex-membered set
B is ext-real set
{B} is non empty ext-real-membered set
A is ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real set
a is ext-real set
a * B is ext-real set
(A,a) is set
{a} is non empty ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
{ (B * b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
a is set
z is ext-real Element of ExtREAL
B * z is ext-real set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
a is set
{ (B * b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is non empty ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is ext-real-membered set
B is ext-real-membered set
A /\ B is ext-real-membered set
a is complex real ext-real set
((A /\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A /\ B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A /\ B ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) /\ (B,a) is ext-real-membered set
z is ext-real set
c2 is ext-real Element of ExtREAL
a * c2 is ext-real set
w3 is ext-real Element of ExtREAL
a * w3 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
a is ext-real set
(A,a) is ext-real-membered set
{a} is non empty ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
((A \ B),a) is ext-real-membered set
({a},(A \ B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \ B ) } is set
z is ext-real set
c2 is ext-real Element of ExtREAL
a * c2 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
a is complex real ext-real set
((A \ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A \ B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \ B ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
z is ext-real set
c2 is ext-real Element of ExtREAL
a * c2 is ext-real set
w3 is ext-real Element of ExtREAL
a * w3 is ext-real set
A is ext-real-membered set
B is ext-real-membered set
A \+\ B is ext-real-membered set
A \ B is ext-real-membered set
B \ A is ext-real-membered set
(A \ B) \/ (B \ A) is ext-real-membered set
a is complex real ext-real set
((A \+\ B),a) is ext-real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},(A \+\ B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \+\ B ) } is set
(A,a) is ext-real-membered set
({a},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is ext-real-membered set
({a},B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \+\ (B,a) is ext-real-membered set
(A,a) \ (B,a) is ext-real-membered set
(B,a) \ (A,a) is ext-real-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is ext-real-membered set
A \ B is ext-real-membered Element of K13(A)
K13(A) is set
((A \ B),a) is ext-real-membered set
({a},(A \ B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A \ B ) } is set
B \ A is ext-real-membered Element of K13(B)
K13(B) is set
((B \ A),a) is ext-real-membered set
({a},(B \ A)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in B \ A ) } is set
((A \ B),a) \/ ((B \ A),a) is ext-real-membered set
(A,a) \ (B,a) is ext-real-membered Element of K13((A,a))
K13((A,a)) is set
((A,a) \ (B,a)) \/ ((B \ A),a) is ext-real-membered set
B is complex set
{B} is non empty complex-membered set
A is complex-membered set
({B},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered set
B is complex set
a is complex set
a * B is complex Element of COMPLEX
(A,a) is set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
{ (B * b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
a is set
z is complex Element of COMPLEX
B * z is complex Element of COMPLEX
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
a is set
{ (B * b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is non empty complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex real ext-real set
(A,B) is complex-membered set
{B} is non empty complex-membered ext-real-membered real-membered set
({B},A) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex real rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered rational-membered integer-membered set
B is complex real integer rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered rational-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
B is complex epsilon-transitive epsilon-connected ordinal natural real integer rational ext-real non negative set
(A,B) is complex-membered ext-real-membered real-membered rational-membered integer-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
({B},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in A ) } is set
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
a is complex real ext-real set
z is ext-real set
(A,a) is complex-membered ext-real-membered real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
({a},A) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in A ) } is set
(B,z) is ext-real-membered set
{z} is non empty ext-real-membered set
({z},B) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {z} & b₂ in B ) } is set
(A,a) is ext-real-membered set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
z is complex set
a * z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
a * c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
A is complex-membered set
B is complex-membered set
A /\ B is complex-membered set
a is complex set
((A /\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A /\ B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A /\ B ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
(A,a) /\ (B,a) is complex-membered set
z is complex set
c2 is complex Element of COMPLEX
a * c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
a * w3 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
a is complex set
((A \ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \ B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A \ B ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
z is complex set
c2 is complex Element of COMPLEX
a * c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
a * w3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
a * c2 is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
a is complex set
((A \+\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \+\ B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A \+\ B ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
(A,a) \+\ (B,a) is complex-membered set
(A,a) \ (B,a) is complex-membered set
(B,a) \ (A,a) is complex-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
((A \ B),a) is complex-membered set
({a},(A \ B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A \ B ) } is set
B \ A is complex-membered Element of K13(B)
K13(B) is set
((B \ A),a) is complex-membered set
({a},(B \ A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B \ A ) } is set
((A \ B),a) \/ ((B \ A),a) is complex-membered set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
((A,a) \ (B,a)) \/ ((B \ A),a) is complex-membered set
{0} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
A is complex-membered set
(A,0) is complex-membered set
({0},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {0} & b₂ in A ) } is set
B is complex set
a is complex Element of COMPLEX
z is complex Element of COMPLEX
a * z is complex Element of COMPLEX
{} is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
A is complex-membered set
(A,0) is complex-membered set
({0},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {0} & b₂ in A ) } is set
the complex Element of A is complex Element of A
a is complex epsilon-transitive epsilon-connected ordinal natural real integer rational ext-real non negative set
0 * the complex Element of A is complex Element of COMPLEX
{ (0 * b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
1 is complex non empty epsilon-transitive epsilon-connected ordinal natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered ext-real positive non negative Element of NAT
A is complex-membered set
(A,1) is complex-membered set
{1} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
({1},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {1} & b₂ in A ) } is set
B is complex set
a is complex Element of COMPLEX
z is complex Element of COMPLEX
a * z is complex Element of COMPLEX
1 * B is complex Element of COMPLEX
{ (1 * b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex-membered set
B is complex set
a is complex set
B * a is complex Element of COMPLEX
(A,(B * a)) is complex-membered set
{(B * a)} is non empty complex-membered set
({(B * a)},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(B * a)} & b₂ in A ) } is set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
((A,a),B) is complex-membered set
{B} is non empty complex-membered set
({B},(A,a)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A,a) ) } is set
({B},{a}) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in {a} ) } is set
(({B},{a}),A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in ({B},{a}) & b₂ in A ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex set
((A,B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A,B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A,B) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
((A,a),B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in B ) } is set
A is complex-membered set
B is complex set
(A,B) is complex-membered set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
a is complex set
B + a is complex Element of COMPLEX
(A,(B + a)) is complex-membered set
{(B + a)} is non empty complex-membered set
({(B + a)},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(B + a)} & b₂ in A ) } is set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
((A,B),(A,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (A,a) ) } is set
({B},{a}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in {a} ) } is set
A is complex-membered set
B is complex set
(A,B) is complex-membered set
{B} is non empty complex-membered set
({B},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in A ) } is set
a is complex set
B - a is complex Element of COMPLEX
- a is complex set
B + (- a) is complex set
(A,(B - a)) is complex-membered set
{(B - a)} is non empty complex-membered set
({(B - a)},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(B - a)} & b₂ in A ) } is set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
((A,B),(A,a)) is complex-membered set
((A,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) } is set
((A,B),((A,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in ((A,a)) ) } is set
({B},{a}) is non empty complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
({B},({a})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in ({a}) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex set
((A,B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A,B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A,B) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
((A,a),(B,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in (B,a) ) } is set
z is complex set
c2 is complex Element of COMPLEX
w3 is complex Element of COMPLEX
c2 + w3 is complex Element of COMPLEX
c3 is complex Element of COMPLEX
a * c3 is complex Element of COMPLEX
c2 is complex Element of COMPLEX
a * c2 is complex Element of COMPLEX
c2 + c3 is complex Element of COMPLEX
a * (c2 + c3) is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex set
((A,B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A,B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A,B) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in A ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in B ) } is set
((A,a),(B,a)) is complex-membered set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
((A,a),((B,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in ((B,a)) ) } is set
((B),a) is complex-membered set
({a},(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
((A,a),((B),a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in ((B),a) ) } is set
B is ext-real set
{B} is non empty ext-real-membered set
A is ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
A is ext-real-membered set
B is ext-real set
a is ext-real set
a / B is ext-real set
B " is ext-real set
a * (B ") is ext-real set
(A,a) is set
{a} is non empty ext-real-membered set
({a},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {a} & b₂ in (A) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
{ (B / b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(w3) is ext-real Element of ExtREAL
(z,(w3)) is ext-real Element of ExtREAL
z / w3 is ext-real set
w3 " is ext-real set
z * (w3 ") is ext-real set
a is set
z is ext-real Element of ExtREAL
B / z is ext-real set
z " is ext-real set
B * (z ") is ext-real set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
a is set
{ (B / b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
A is non empty ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is non empty ext-real-membered set
(A) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
({B},A) is ext-real-membered set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {B} & b₂ in (A) ) } is set
B is complex set
{B} is non empty complex-membered set
A is complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is complex-membered set
B is complex set
a is complex set
a / B is complex Element of COMPLEX
B " is complex set
a * (B ") is complex set
(A,a) is set
{a} is non empty complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
{ (B / b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
c2 " is complex Element of COMPLEX
z / (c2 ") is complex Element of COMPLEX
(c2 ") " is complex set
z * ((c2 ") ") is complex set
a is set
z is complex Element of COMPLEX
B / z is complex Element of COMPLEX
z " is complex set
B * (z ") is complex set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
a is set
{ (B / b₁) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is non empty complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is non empty complex-membered set
(A) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex real ext-real set
(A,B) is complex-membered set
{B} is non empty complex-membered ext-real-membered real-membered set
({B},A) is complex-membered ext-real-membered real-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
({B},(A)) is ext-real-membered set
({B},A) is ext-real-membered set
({B},(A)) is ext-real-membered set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex real rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered set
({B},A) is complex-membered ext-real-membered real-membered rational-membered set
(A) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({B},(A)) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
({B},(A)) is ext-real-membered set
({B},A) is ext-real-membered set
({B},(A)) is ext-real-membered set
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
a is complex real ext-real set
z is ext-real set
(A,a) is complex-membered ext-real-membered real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
({a},A) is complex-membered ext-real-membered real-membered set
(A) is complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
(A) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
({a},(A)) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
({a},(A)) is ext-real-membered set
({a},A) is ext-real-membered set
({a},(A)) is ext-real-membered set
(B,z) is ext-real-membered set
{z} is non empty ext-real-membered set
({z},B) is ext-real-membered set
(B) is ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in B } is set
({z},(B)) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in {z} & b₂ in (B) ) } is set
(A,a) is ext-real-membered set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
z is complex set
a / z is complex Element of COMPLEX
z " is complex set
a * (z ") is complex set
c2 is complex Element of COMPLEX
a / c2 is complex Element of COMPLEX
c2 " is complex set
a * (c2 ") is complex set
z " is complex Element of COMPLEX
c2 " is complex Element of COMPLEX
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
A is complex-membered set
B is complex-membered set
A /\ B is complex-membered set
a is complex set
((A /\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A /\ B)) is complex-membered set
((A /\ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A /\ B } is set
({a},((A /\ B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A /\ B)) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) /\ (B,a) is complex-membered set
(A) /\ (B) is complex-membered set
(((A) /\ (B)),a) is complex-membered set
({a},((A) /\ (B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) /\ (B) ) } is set
((A),a) is complex-membered set
((B),a) is complex-membered set
((A),a) /\ ((B),a) is complex-membered set
A is complex-membered set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
a is complex set
((A \ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \ B)) is complex-membered set
((A \ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A \ B } is set
({a},((A \ B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A \ B)) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
(A) \ (B) is complex-membered Element of K13((A))
K13((A)) is set
(((A) \ (B)),a) is complex-membered set
({a},((A) \ (B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) \ (B) ) } is set
((A),a) is complex-membered set
((B),a) is complex-membered set
((A),a) \ ((B),a) is complex-membered Element of K13(((A),a))
K13(((A),a)) is set
A is complex-membered set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
a is complex set
((A \+\ B),a) is complex-membered set
{a} is non empty complex-membered set
({a},(A \+\ B)) is complex-membered set
((A \+\ B)) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A \+\ B } is set
({a},((A \+\ B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in ((A \+\ B)) ) } is set
(A,a) is complex-membered set
({a},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
(B,a) is complex-membered set
({a},B) is complex-membered set
(B) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in B } is set
({a},(B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (B) ) } is set
(A,a) \+\ (B,a) is complex-membered set
(A,a) \ (B,a) is complex-membered set
(B,a) \ (A,a) is complex-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is complex-membered set
(A) \+\ (B) is complex-membered set
(A) \ (B) is complex-membered set
(B) \ (A) is complex-membered set
((A) \ (B)) \/ ((B) \ (A)) is complex-membered set
(((A) \+\ (B)),a) is complex-membered set
({a},((A) \+\ (B))) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) \+\ (B) ) } is set
((A),a) is complex-membered set
((B),a) is complex-membered set
((A),a) \+\ ((B),a) is complex-membered set
((A),a) \ ((B),a) is complex-membered set
((B),a) \ ((A),a) is complex-membered set
(((A),a) \ ((B),a)) \/ (((B),a) \ ((A),a)) is complex-membered set
A is complex-membered set
B is complex set
(A,B) is complex-membered set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
a is complex set
B + a is complex Element of COMPLEX
(A,(B + a)) is complex-membered set
{(B + a)} is non empty complex-membered set
({(B + a)},A) is complex-membered set
({(B + a)},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(B + a)} & b₂ in (A) ) } is set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
((A,B),(A,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in (A,a) ) } is set
({B},{a}) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in {a} ) } is set
A is complex-membered set
B is complex set
(A,B) is complex-membered set
{B} is non empty complex-membered set
({B},A) is complex-membered set
(A) is complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in A } is set
({B},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in (A) ) } is set
a is complex set
B - a is complex Element of COMPLEX
- a is complex set
B + (- a) is complex set
(A,(B - a)) is complex-membered set
{(B - a)} is non empty complex-membered set
({(B - a)},A) is complex-membered set
({(B - a)},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(B - a)} & b₂ in (A) ) } is set
(A,a) is complex-membered set
{a} is non empty complex-membered set
({a},A) is complex-membered set
({a},(A)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {a} & b₂ in (A) ) } is set
((A,B),(A,a)) is complex-membered set
((A,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (A,a) } is set
((A,B),((A,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in ((A,a)) ) } is set
({B},{a}) is non empty complex-membered set
({a}) is non empty complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
({B},({a})) is non empty complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {B} & b₂ in ({a}) ) } is set
A is ext-real-membered set
B is ext-real set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is ext-real-membered set
B is ext-real set
a is ext-real set
B / a is ext-real set
a " is ext-real set
B * (a ") is ext-real set
(A,a) is set
{a} is non empty ext-real-membered set
(A,{a}) is ext-real-membered set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
(A,({a})) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({a}) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
{ (b₁ / B) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
a is set
z is ext-real Element of ExtREAL
c2 is ext-real Element of ExtREAL
(z,c2) is ext-real Element of ExtREAL
w3 is ext-real Element of ExtREAL
(w3) is ext-real Element of ExtREAL
(z,(w3)) is ext-real Element of ExtREAL
z / w3 is ext-real set
w3 " is ext-real set
z * (w3 ") is ext-real set
a is set
z is ext-real Element of ExtREAL
z / B is ext-real set
B " is ext-real set
z * (B ") is ext-real set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
a is set
{ (b₁ / B) where b₁ is ext-real Element of ExtREAL : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is non empty ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is non empty ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is non empty ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is ext-real-membered set
B is ext-real set
(A,B) is set
{B} is non empty ext-real-membered set
(A,{B}) is ext-real-membered set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in A & b₂ in ({B}) ) } is set
A is complex-membered set
B is complex set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is complex-membered set
B is complex set
a is complex set
B / a is complex Element of COMPLEX
a " is complex set
B * (a ") is complex set
(A,a) is set
{a} is non empty complex-membered set
(A,{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
{ (b₁ / B) where b₁ is complex Element of COMPLEX : b₁ in A } is set
a is set
z is complex Element of COMPLEX
c2 is complex Element of COMPLEX
z * c2 is complex Element of COMPLEX
B " is complex Element of COMPLEX
{(B ")} is non empty complex-membered set
c2 " is complex Element of COMPLEX
z / (c2 ") is complex Element of COMPLEX
(c2 ") " is complex set
z * ((c2 ") ") is complex set
a is set
z is complex Element of COMPLEX
z / B is complex Element of COMPLEX
B " is complex set
z * (B ") is complex set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
a is set
{ (b₁ / B) where b₁ is complex Element of COMPLEX : b₁ in A } is set
A is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
({B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V21() ext-real non negative set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is non empty complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is non empty complex-membered set
({B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is non empty complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is complex-membered set
B is complex set
(A,B) is set
{B} is non empty complex-membered set
(A,{B}) is complex-membered set
({B}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
(A,({B})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
A is complex-membered ext-real-membered real-membered set
B is complex real ext-real set
(A,B) is complex-membered set
{B} is non empty complex-membered ext-real-membered real-membered set
(A,{B}) is complex-membered ext-real-membered real-membered set
({B}) is non empty complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
(A,({B})) is ext-real-membered set
(A,{B}) is ext-real-membered set
(A,({B})) is ext-real-membered set
A is complex-membered ext-real-membered real-membered rational-membered set
B is complex real rational ext-real set
(A,B) is complex-membered ext-real-membered real-membered set
{B} is non empty complex-membered ext-real-membered real-membered rational-membered set
(A,{B}) is complex-membered ext-real-membered real-membered rational-membered set
({B}) is non empty complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {B} } is set
({B}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {B} } is set
(A,({B})) is complex-membered ext-real-membered real-membered rational-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({B}) ) } is set
(A,({B})) is ext-real-membered set
(A,{B}) is ext-real-membered set
(A,({B})) is ext-real-membered set
A is complex-membered ext-real-membered real-membered set
B is ext-real-membered set
a is complex real ext-real set
z is ext-real set
(A,a) is complex-membered ext-real-membered real-membered set
{a} is non empty complex-membered ext-real-membered real-membered set
(A,{a}) is complex-membered ext-real-membered real-membered set
({a}) is non empty complex-membered ext-real-membered real-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
({a}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {a} } is set
(A,({a})) is complex-membered ext-real-membered real-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(A,({a})) is ext-real-membered set
(A,{a}) is ext-real-membered set
(A,({a})) is ext-real-membered set
(B,z) is ext-real-membered set
{z} is non empty ext-real-membered set
(B,{z}) is ext-real-membered set
({z}) is non empty ext-real-membered set
{ (b₁) where b₁ is ext-real Element of ExtREAL : b₁ in {z} } is set
(B,({z})) is ext-real-membered set
{ (b₁,b₂) where b₁, b₂ is ext-real Element of ExtREAL : ( b₁ in B & b₂ in ({z}) ) } is set
(A,a) is ext-real-membered set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
(A,{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
z is complex set
z / a is complex Element of COMPLEX
a " is complex set
z * (a ") is complex set
c2 is complex Element of COMPLEX
c2 / a is complex Element of COMPLEX
c2 * (a ") is complex set
A is complex-membered set
B is complex-membered set
a is complex set
(A,a) is complex-membered set
{a} is non empty complex-membered set
(A,{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
A is complex-membered set
B is complex-membered set
A /\ B is complex-membered set
a is complex set
((A /\ B),a) is complex-membered set
{a} is non empty complex-membered set
((A /\ B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A /\ B),({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A /\ B & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) /\ (B,a) is complex-membered set
a " is complex Element of COMPLEX
{(a ")} is non empty complex-membered set
((A /\ B),(a ")) is complex-membered set
({(a ")},(A /\ B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in A /\ B ) } is set
(A,(a ")) is complex-membered set
({(a ")},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in A ) } is set
(B,(a ")) is complex-membered set
({(a ")},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in B ) } is set
(A,(a ")) /\ (B,(a ")) is complex-membered set
A is complex-membered set
B is complex-membered set
A \ B is complex-membered Element of K13(A)
K13(A) is set
a is complex set
((A \ B),a) is complex-membered set
{a} is non empty complex-membered set
((A \ B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A \ B),({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A \ B & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) \ (B,a) is complex-membered Element of K13((A,a))
K13((A,a)) is set
a " is complex Element of COMPLEX
{(a ")} is non empty complex-membered set
((A \ B),(a ")) is complex-membered set
({(a ")},(A \ B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in A \ B ) } is set
(A,(a ")) is complex-membered set
({(a ")},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in A ) } is set
(B,(a ")) is complex-membered set
({(a ")},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in B ) } is set
(A,(a ")) \ (B,(a ")) is complex-membered Element of K13((A,(a ")))
K13((A,(a "))) is set
A is complex-membered set
B is complex-membered set
A \+\ B is complex-membered set
A \ B is complex-membered set
B \ A is complex-membered set
(A \ B) \/ (B \ A) is complex-membered set
a is complex set
((A \+\ B),a) is complex-membered set
{a} is non empty complex-membered set
((A \+\ B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A \+\ B),({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A \+\ B & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
(A,a) \+\ (B,a) is complex-membered set
(A,a) \ (B,a) is complex-membered set
(B,a) \ (A,a) is complex-membered set
((A,a) \ (B,a)) \/ ((B,a) \ (A,a)) is complex-membered set
a " is complex Element of COMPLEX
{(a ")} is non empty complex-membered set
((A \+\ B),(a ")) is complex-membered set
({(a ")},(A \+\ B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in A \+\ B ) } is set
(A,(a ")) is complex-membered set
({(a ")},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in A ) } is set
(B,(a ")) is complex-membered set
({(a ")},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in B ) } is set
(A,(a ")) \+\ (B,(a ")) is complex-membered set
(A,(a ")) \ (B,(a ")) is complex-membered set
(B,(a ")) \ (A,(a ")) is complex-membered set
((A,(a ")) \ (B,(a "))) \/ ((B,(a ")) \ (A,(a "))) is complex-membered set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in B ) } is set
a is complex set
((A,B),a) is complex-membered set
{a} is non empty complex-membered set
((A,B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A,B),({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
((A,a),(B,a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in (B,a) ) } is set
a " is complex Element of COMPLEX
((A,B),(a ")) is complex-membered set
{(a ")} is non empty complex-membered set
({(a ")},(A,B)) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in (A,B) ) } is set
(A,(a ")) is complex-membered set
({(a ")},A) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in A ) } is set
(B,(a ")) is complex-membered set
({(a ")},B) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in {(a ")} & b₂ in B ) } is set
((A,(a ")),(B,(a "))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,(a ")) & b₂ in (B,(a ")) ) } is set
((A,a),(B,(a "))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in (B,(a ")) ) } is set
A is complex-membered set
B is complex-membered set
(A,B) is complex-membered set
(B) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in B } is set
(A,(B)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in (B) ) } is set
a is complex set
((A,B),a) is complex-membered set
{a} is non empty complex-membered set
((A,B),{a}) is complex-membered set
({a}) is non empty complex-membered set
{ (b₁ ") where b₁ is complex Element of COMPLEX : b₁ in {a} } is set
((A,B),({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,B) & b₂ in ({a}) ) } is set
(A,a) is complex-membered set
(A,{a}) is complex-membered set
(A,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in A & b₂ in ({a}) ) } is set
(B,a) is complex-membered set
(B,{a}) is complex-membered set
(B,({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in B & b₂ in ({a}) ) } is set
((A,a),(B,a)) is complex-membered set
((B,a)) is complex-membered set
{ (- b₁) where b₁ is complex Element of COMPLEX : b₁ in (B,a) } is set
((A,a),((B,a))) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in ((B,a)) ) } is set
((B),a) is complex-membered set
((B),{a}) is complex-membered set
((B),({a})) is complex-membered set
{ (b₁ * b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (B) & b₂ in ({a}) ) } is set
((A,a),((B),a)) is complex-membered set
{ (b₁ + b₂) where b₁, b₂ is complex Element of COMPLEX : ( b₁ in (A,a) & b₂ in ((B),a) ) } is set