Nuprl Lemma : qless_wf
∀[r,s:ℚ]. (r < s ∈ ℙ)
Proof
Definitions occuring in Statement :
qless: r < s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
qless: r < s,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t)
Lemmas referenced :
grp_lt_wf,
qadd_grp_wf2,
ocgrp_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[r,s:\mBbbQ{}]. (r < s \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-10_45_04
Last ObjectModification:
2015_12_27-PM-07_53_53
Theory : rationals
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