Nuprl Lemma : rioint_wf
∀[u:ℝ]. ((-∞, u) ∈ Interval)
Proof
Definitions occuring in Statement :
rioint: (-∞, u),
interval: Interval,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
rioint: (-∞, u),
interval: Interval,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
it_wf,
unit_wf2,
real_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairEquality,
inrEquality,
lemma_by_obid,
hypothesis,
applyEquality,
thin,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalHypSubstitution,
unionEquality,
inlEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[u:\mBbbR{}]. ((-\minfty{}, u) \mmember{} Interval)
Date html generated:
2016_05_18-AM-08_36_56
Last ObjectModification:
2015_12_27-PM-11_52_47
Theory : reals
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