Nuprl Lemma : sq_stable__ifun
∀[I:Interval]. ∀[f:I ⟶ℝ]. SqStable(ifun(f;I)) supposing icompact(I)
Proof
Definitions occuring in Statement :
ifun: ifun(f;I),
icompact: icompact(I),
rfun: I ⟶ℝ,
interval: Interval,
sq_stable: SqStable(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
ifun: ifun(f;I),
icompact: icompact(I),
and: P ∧ Q
Lemmas referenced :
icompact_wf,
rfun_wf,
interval_wf,
sq_stable__real-fun,
left-endpoint_wf,
right-endpoint_wf,
icompact-is-rccint
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
hypothesisEquality,
independent_isectElimination,
productElimination,
sqequalRule
Latex:
\mforall{}[I:Interval]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. SqStable(ifun(f;I)) supposing icompact(I)
Date html generated:
2016_10_26-AM-09_48_09
Last ObjectModification:
2016_08_18-PM-02_55_07
Theory : reals
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