Nuprl Lemma : qrle_wf
∀[x,y:[ℝ]]. (qrle(x;y) ∈ ℙ)
Proof
Definitions occuring in Statement :
qrle: qrle(x;y),
qreal: [ℝ],
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qrle: qrle(x;y),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
squash_wf,
exists_wf,
real_wf,
and_wf,
equal_wf,
qreal_wf,
real-subtype-qreal,
rleq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[x,y:[\mBbbR{}]]. (qrle(x;y) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-11_15_27
Last ObjectModification:
2015_12_27-PM-10_39_00
Theory : reals
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