Nuprl Lemma : ss-homeo_weakening
∀[X,Y:SeparationSpace]. ss-homeo(X;Y) supposing X = Y ∈ SeparationSpace
Proof
Definitions occuring in Statement :
ss-homeo: ss-homeo(X;Y),
separation-space: SeparationSpace,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ss-homeo: ss-homeo(X;Y),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
cand: A c∧ B,
implies: P ⇒ Q,
ss-eq: x ≡ y,
not: ¬A,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
ss-id_wf,
subtype_rel-equal,
ss-point_wf,
ss-fun_wf,
and_wf,
equal_wf,
separation-space_wf,
ss_ap_id_lemma,
ss-eq_weakening,
ss-sep_wf,
all_wf,
ss-eq_wf,
ss-ap_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
dependent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
independent_isectElimination,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
instantiate,
applyLambdaEquality,
setElimination,
productElimination,
equalityTransitivity,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
lambdaFormation,
independent_functionElimination,
lambdaEquality,
productEquality
Latex:
\mforall{}[X,Y:SeparationSpace]. ss-homeo(X;Y) supposing X = Y
Date html generated:
2020_05_20-PM-01_19_55
Last ObjectModification:
2018_07_04-PM-11_25_37
Theory : intuitionistic!topology
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