Nuprl Lemma : rless-content
∀[x:ℝ]. ∀[y:{y:ℝ| x < y} ]. (rlessw(x;y) ∈ x < y)
Proof
Definitions occuring in Statement :
rlessw: rlessw(x;y),
rless: x < y,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rlessw_wf,
set_wf,
real_wf,
rless_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectElimination,
lambdaEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[y:\{y:\mBbbR{}| x < y\} ]. (rlessw(x;y) \mmember{} x < y)
Date html generated:
2016_05_18-AM-07_04_22
Last ObjectModification:
2015_12_28-AM-00_35_39
Theory : reals
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