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ThmDex – An index of mathematical definitions, results, and conjectures.
Definitions
,
Results
,
Conjectures
Result R1034 on
D80: Power set
Power set is closed under unions
Formulation 0
Let
X
be a
D11: Set
.
Let
E
j
be a
D11: Set
for each
j
∈
J
.
Then
∀
j
∈
J
:
E
j
∈
P
(
X
)
⇒
⋃
j
∈
J
E
j
∈
P
(
X
)
Formulation 1
Let
X
be a
D11: Set
.
Let
E
j
be a
D11: Set
for each
j
∈
J
.
Then
∀
j
∈
J
:
E
j
⊆
X
⇒
⋃
j
∈
J
E
j
⊆
X
Proofs
Proof 0
Let
X
be a
D11: Set
.
Let
E
j
be a
D11: Set
for each
j
∈
J
.
Corollary to
R2071: Isotonicity of set union
.
◻