Nuprl Lemma : q_less_wf
ā[a,b:ā]. (q_less(a;b) ā š¹)
Proof
Definitions occuring in Statement :
q_less: q_less(r;s)
,
rationals: ā
,
bool: š¹
,
uall: ā[x:A]. B[x]
,
member: t ā T
Definitions unfolded in proof :
uall: ā[x:A]. B[x]
,
member: t ā T
,
q_less: q_less(r;s)
,
subtype_rel: A ār B
,
ocgrp: OGrp
,
ocmon: OCMon
,
abmonoid: AbMon
,
mon: Mon
,
oset_of_ocmon: gāoset
,
dset_of_mon: gāset
,
set_car: |p|
,
pi1: fst(t)
,
qadd_grp: <ā+>
,
grp_car: |g|
Lemmas referenced :
rational_set_blt,
set_blt_wf,
oset_of_ocmon_wf0,
qadd_grp_wf2,
ocgrp_wf,
rationals_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[a,b:\mBbbQ{}]. (q\_less(a;b) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-10_57_22
Last ObjectModification:
2015_12_27-PM-07_52_04
Theory : rationals
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