Nuprl Lemma : rless_wf
∀[x,y:ℝ]. (x < y ∈ ℙ)
Proof
Definitions occuring in Statement :
rless: x < y,
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rless: x < y,
so_lambda: λ2x.t[x],
real: ℝ,
so_apply: x[s]
Lemmas referenced :
sq_exists_wf,
nat_plus_wf,
less_than_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
addEquality,
applyEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x,y:\mBbbR{}]. (x < y \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_03_09
Last ObjectModification:
2015_12_28-AM-00_34_47
Theory : reals
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