Nuprl Lemma : ss-homeo_inversion
∀[X,Y:SeparationSpace]. (ss-homeo(X;Y) ⇒ ss-homeo(Y;X))
Proof
Definitions occuring in Statement :
ss-homeo: ss-homeo(X;Y),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
ss-homeo: ss-homeo(X;Y),
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
ss-point_wf,
ss-eq_wf,
ss-ap_wf,
exists_wf,
ss-fun_wf,
ss-homeo_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
independent_pairFormation,
hypothesis,
productEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
sqequalRule,
lambdaEquality
Latex:
\mforall{}[X,Y:SeparationSpace]. (ss-homeo(X;Y) {}\mRightarrow{} ss-homeo(Y;X))
Date html generated:
2020_05_20-PM-01_19_56
Last ObjectModification:
2018_07_04-PM-11_26_53
Theory : intuitionistic!topology
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