Nuprl Lemma : left-endpoint_wf
∀[I:Interval]. left-endpoint(I) ∈ ℝ supposing i-finite(I)
Proof
Definitions occuring in Statement :
left-endpoint: left-endpoint(I),
i-finite: i-finite(I),
interval: Interval,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
left-endpoint: left-endpoint(I),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
top: Top,
prop: ℙ
Lemmas referenced :
pi1_wf_top,
real_wf,
endpoints_wf,
subtype_rel_product,
top_wf,
i-finite_wf,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
independent_isectElimination,
applyEquality,
lambdaEquality,
because_Cache,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[I:Interval]. left-endpoint(I) \mmember{} \mBbbR{} supposing i-finite(I)
Date html generated:
2016_05_18-AM-08_17_42
Last ObjectModification:
2015_12_27-PM-11_56_33
Theory : reals
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