Nuprl Lemma : sq_stable__i-member
∀I:Interval. ∀r:ℝ. SqStable(r ∈ I)
Proof
Definitions occuring in Statement :
i-member: r ∈ I,
interval: Interval,
real: ℝ,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
interval: Interval,
i-member: r ∈ I,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
sq_stable__and,
rleq_wf,
sq_stable__rleq,
rless_wf,
sq_stable__rless,
sq_stable_from_decidable,
true_wf,
decidable__true,
real_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
sqequalRule,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
isect_memberEquality,
independent_functionElimination,
because_Cache,
dependent_functionElimination
Latex:
\mforall{}I:Interval. \mforall{}r:\mBbbR{}. SqStable(r \mmember{} I)
Date html generated:
2016_05_18-AM-08_19_30
Last ObjectModification:
2015_12_27-PM-11_58_06
Theory : reals
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