Nuprl Lemma : sq_stable__ss-eq
∀[ss:SeparationSpace]. ∀[x,y:Point]. SqStable(x ≡ y)
Proof
Definitions occuring in Statement :
ss-eq: x ≡ y,
ss-point: Point,
separation-space: SeparationSpace,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
prop: ℙ,
false: False,
not: ¬A,
ss-eq: x ≡ y,
sq_stable: SqStable(P),
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
ss-point_wf,
squash_wf,
ss-sep_wf,
stable__ss-eq,
ss-eq_wf,
sq_stable__from_stable
Rules used in proof :
voidElimination,
isect_memberEquality,
because_Cache,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
independent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[ss:SeparationSpace]. \mforall{}[x,y:Point]. SqStable(x \mequiv{} y)
Date html generated:
2016_11_08-AM-09_11_01
Last ObjectModification:
2016_10_31-PM-01_50_33
Theory : inner!product!spaces
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