Nuprl Lemma : ss-point_wf
∀[ss:SeparationSpace]. (Point ∈ Type)
Proof
Definitions occuring in Statement :
ss-point: Point,
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
or: P ∨ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
subtype_rel: A ⊆r B,
record-select: r.x,
record+: record+,
separation-space: SeparationSpace,
ss-point: Point,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
separation-space_wf,
or_wf,
not_wf,
all_wf,
subtype_rel_self
Rules used in proof :
axiomEquality,
rename,
setElimination,
functionExtensionality,
because_Cache,
hypothesisEquality,
cumulativity,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
functionEquality,
setEquality,
universeEquality,
isectElimination,
extract_by_obid,
instantiate,
tokenEquality,
applyEquality,
hypothesis,
thin,
dependentIntersectionEqElimination,
dependentIntersectionElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[ss:SeparationSpace]. (Point \mmember{} Type)
Date html generated:
2016_11_08-AM-09_10_43
Last ObjectModification:
2016_10_31-AM-11_00_51
Theory : inner!product!spaces
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