Nuprl Lemma : decidable__oal_lt
∀s:LOSet. ∀g:OGrp. ∀ps,qs:|oal(s;g)|. Dec(ps << qs)
Proof
Definitions occuring in Statement :
oal_lt: ps << qs,
oalist: oal(a;b),
decidable: Dec(P),
all: ∀x:A. B[x],
ocgrp: OGrp,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
ocgrp: OGrp,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
decidable_functionality,
oal_lt_wf,
assert_wf,
oal_blt_wf,
ocgrp_subtype_abdgrp,
assert_of_oal_blt,
decidable__assert,
set_car_wf,
oalist_wf,
ocmon_subtype_abdmonoid,
ocgrp_subtype_ocmon,
subtype_rel_transitivity,
ocgrp_wf,
ocmon_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
setElimination,
rename,
hypothesis,
applyEquality,
sqequalRule,
independent_functionElimination,
productElimination,
independent_pairFormation,
because_Cache,
instantiate,
independent_isectElimination
Latex:
\mforall{}s:LOSet. \mforall{}g:OGrp. \mforall{}ps,qs:|oal(s;g)|. Dec(ps << qs)
Date html generated:
2016_05_16-AM-08_21_03
Last ObjectModification:
2015_12_28-PM-06_25_04
Theory : polynom_2
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