Nuprl Lemma : ss-mem-open_wf
∀[X:SeparationSpace]. ∀[O:Open(X)]. ∀[x:Point(X)]. (x ∈ O ∈ ℙ)
Proof
Definitions occuring in Statement :
ss-mem-open: x ∈ O,
ss-open: Open(X),
ss-point: Point(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ss-mem-open: x ∈ O,
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,
ss-mem-basic_wf,
ss-point_wf,
ss-open_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
productEquality,
applyEquality,
instantiate,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[O:Open(X)]. \mforall{}[x:Point(X)]. (x \mmember{} O \mmember{} \mBbbP{})
Date html generated:
2020_05_20-PM-01_22_03
Last ObjectModification:
2018_07_06-PM-01_55_22
Theory : intuitionistic!topology
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