Nuprl Lemma : interval-ss_wf
∀[I:Interval]. (interval-ss(I) ∈ SeparationSpace)
Proof
Definitions occuring in Statement :
interval-ss: interval-ss(I),
separation-space: SeparationSpace,
interval: Interval,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
real: ℝ,
btrue: tt,
bfalse: ff,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-update: r[x := v],
mk-ss: Point=P #=Sep symm=Sym cotrans=C,
real-ss: ℝ,
record-select: r.x,
ss-point: Point(ss),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
interval-ss: interval-ss(I),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
interval_wf,
ss-point_wf,
real_wf,
subtype_rel_self,
i-member_wf,
real-ss_wf,
set-ss_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:Interval]. (interval-ss(I) \mmember{} SeparationSpace)
Date html generated:
2018_07_29-AM-10_11_33
Last ObjectModification:
2018_06_28-PM-05_30_01
Theory : constructive!algebra
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