Nuprl Lemma : ss-open_wf
∀[X:SeparationSpace]. (Open(X) ∈ 𝕌')
Proof
Definitions occuring in Statement :
ss-open: Open(X),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ss-open: Open(X),
prop: ℙ
Lemmas referenced :
ss-basic_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
functionEquality,
cumulativity,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:SeparationSpace]. (Open(X) \mmember{} \mBbbU{}')
Date html generated:
2020_05_20-PM-01_21_58
Last ObjectModification:
2018_07_06-PM-01_51_44
Theory : intuitionistic!topology
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