Nuprl Lemma : ss-open-and_wf
∀[X:SeparationSpace]. ∀[A,B:Open(X)]. (A ⋂ B ∈ Open(X))
Proof
Definitions occuring in Statement :
ss-open-and: A ⋂ B,
ss-open: Open(X),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ss-open-and: A ⋂ B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
ss-open: Open(X),
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
exists_wf,
ss-basic_wf,
subtype_rel_self,
equal_wf,
ss-basic-and_wf,
ss-open_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productEquality,
applyEquality,
instantiate,
universeEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[A,B:Open(X)]. (A \mcap{} B \mmember{} Open(X))
Date html generated:
2020_05_20-PM-01_22_35
Last ObjectModification:
2018_07_06-PM-04_49_20
Theory : intuitionistic!topology
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