Nuprl Lemma : ss-empty_wf
∀[X:SeparationSpace]. (ss-empty() ∈ Open(X))
Proof
Definitions occuring in Statement :
ss-empty: ss-empty(),
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-empty: ss-empty(),
subtype_rel: A ⊆r B,
ss-open: Open(X),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x]
Lemmas referenced :
false_wf,
top_wf,
subtype_rel_dep_function,
ss-basic_wf,
subtype_rel_self,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
hypothesis,
applyEquality,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
cumulativity,
universeEquality,
hypothesisEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[X:SeparationSpace]. (ss-empty() \mmember{} Open(X))
Date html generated:
2020_05_20-PM-01_22_07
Last ObjectModification:
2018_07_06-PM-01_57_55
Theory : intuitionistic!topology
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