Nuprl Lemma : ss-mem-empty
∀[X:SeparationSpace]. ∀[x:Point(X)]. uiff(x ∈ ss-empty();False)
Proof
Definitions occuring in Statement :
ss-empty: ss-empty(),
ss-mem-open: x ∈ O,
ss-point: Point(ss),
separation-space: SeparationSpace,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
false: False
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
ss-empty: ss-empty(),
ss-mem-open: x ∈ O,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
false: False,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
ss-basic_wf,
false_wf,
ss-mem-basic_wf,
ss-point_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
independent_pairFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
voidElimination,
hypothesis,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality,
productEquality,
rename
Latex:
\mforall{}[X:SeparationSpace]. \mforall{}[x:Point(X)]. uiff(x \mmember{} ss-empty();False)
Date html generated:
2020_05_20-PM-01_22_09
Last ObjectModification:
2018_07_06-PM-01_59_50
Theory : intuitionistic!topology
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