Nuprl Lemma : oal_merge_wf2
∀a:LOSet. ∀b:AbDMon. ∀ps,qs:|oal(a;b)|. (ps ++ qs ∈ |oal(a;b)|)
Proof
Definitions occuring in Statement :
oal_merge: ps ++ qs,
oalist: oal(a;b),
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
and: P ∧ Q,
dset_list: s List,
set_prod: s × t,
dset_of_mon: g↓set,
cand: A c∧ B,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
prop: ℙ,
pi2: snd(t),
implies: P ⇒ Q
Lemmas referenced :
set_car_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf,
oal_merge_wf,
assert_wf,
sd_ordered_wf,
map_wf,
grp_car_wf,
not_wf,
mem_wf,
dset_of_mon_wf,
grp_id_wf,
dset_of_mon_wf0,
oal_merge_sd_ordered,
oal_merge_non_id_vals
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
productElimination,
dependent_set_memberEquality,
independent_pairFormation,
productEquality,
independent_functionElimination
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps,qs:|oal(a;b)|. (ps ++ qs \mmember{} |oal(a;b)|)
Date html generated:
2016_05_16-AM-08_18_00
Last ObjectModification:
2015_12_28-PM-06_28_34
Theory : polynom_2
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