Nuprl Lemma : member-i-type
∀[I:Interval]. ∀[r:ℝ]. ∀[p:r ∈ I]. (<i-witness(I;r;p), r> ∈ i-type(I))
Proof
Definitions occuring in Statement :
i-type: i-type(I),
i-witness: i-witness(I;r;p),
i-member: r ∈ I,
interval: Interval,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
pair: <a, b>
Definitions unfolded in proof :
i-type: i-type(I),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
i-witness_wf,
i-witness-property,
i-member_wf,
i-approx_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
dependent_set_memberEquality,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[r:\mBbbR{}]. \mforall{}[p:r \mmember{} I]. (<i-witness(I;r;p), r> \mmember{} i-type(I))
Date html generated:
2016_05_18-AM-08_49_03
Last ObjectModification:
2015_12_27-PM-11_44_20
Theory : reals
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