Nuprl Lemma : ss-homeo_wf
∀[X,Y:SeparationSpace]. (ss-homeo(X;Y) ∈ ℙ)
Proof
Definitions occuring in Statement :
ss-homeo: ss-homeo(X;Y),
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-homeo: ss-homeo(X;Y),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
exists_wf,
ss-point_wf,
ss-fun_wf,
all_wf,
ss-eq_wf,
ss-ap_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,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X,Y:SeparationSpace]. (ss-homeo(X;Y) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-PM-01_19_53
Last ObjectModification:
2018_07_04-PM-00_15_43
Theory : intuitionistic!topology
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