Nuprl Lemma : ifun_wf
∀[I:Interval]. ∀[f:I ⟶ℝ]. ifun(f;I) ∈ ℙ supposing icompact(I)
Proof
Definitions occuring in Statement :
ifun: ifun(f;I),
icompact: icompact(I),
rfun: I ⟶ℝ,
interval: Interval,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ifun: ifun(f;I),
prop: ℙ,
icompact: icompact(I),
and: P ∧ Q
Lemmas referenced :
real-fun_wf,
left-endpoint_wf,
right-endpoint_wf,
icompact_wf,
rfun_wf,
interval_wf,
icompact-is-rccint
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
productElimination
Latex:
\mforall{}[I:Interval]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. ifun(f;I) \mmember{} \mBbbP{} supposing icompact(I)
Date html generated:
2016_10_26-AM-09_47_55
Last ObjectModification:
2016_08_18-PM-02_54_28
Theory : reals
Home
Index