Nuprl Lemma : sq_stable__iproper
∀I:Interval. SqStable(iproper(I))
Proof
Definitions occuring in Statement :
iproper: iproper(I),
interval: Interval,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
iproper: iproper(I),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
sq_stable__all,
i-finite_wf,
rless_wf,
left-endpoint_wf,
right-endpoint_wf,
sq_stable__rless,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}I:Interval. SqStable(iproper(I))
Date html generated:
2016_10_26-AM-09_28_28
Last ObjectModification:
2016_08_24-AM-10_25_23
Theory : reals
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