Nuprl Lemma : qless_witness
∀[r,s:ℚ]. (r < s ⇒ (Ax ∈ r < s))
Proof
Definitions occuring in Statement :
qless: r < s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
axiom: Ax
Definitions unfolded in proof :
qless: r < s,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
ocgrp: OGrp,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
grp_lt: a < b,
set_lt: a <p b,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|
Lemmas referenced :
grp_lt_wf,
qadd_grp_wf2,
ocgrp_wf,
rationals_wf,
assert_witness,
set_blt_wf,
oset_of_ocmon_wf0
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
isect_memberEquality,
independent_functionElimination
Latex:
\mforall{}[r,s:\mBbbQ{}]. (r < s {}\mRightarrow{} (Ax \mmember{} r < s))
Date html generated:
2016_05_15-PM-10_45_07
Last ObjectModification:
2015_12_27-PM-07_53_50
Theory : rationals
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