Nuprl Lemma : lookups_same_a
∀a:LOSet. ∀b:AbDMon. ∀ps,qs:|oal(a;b)|. ((∀u:|a|. ((ps[u]) = (qs[u]) ∈ |b|)) ⇒ (ps = qs ∈ |oal(a;b)|))
Proof
Definitions occuring in Statement :
lookup: as[k],
oalist: oal(a;b),
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T,
abdmonoid: AbDMon,
grp_id: e,
grp_car: |g|,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
dset_list: s List,
set_prod: s × t,
dset_of_mon: g↓set,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
so_lambda: λ2x.t[x],
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
subtype_rel: A ⊆r B,
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
pi2: snd(t)
Lemmas referenced :
all_wf,
set_car_wf,
equal_wf,
grp_car_wf,
lookup_wf,
grp_id_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf,
lookups_same,
assert_wf,
sd_ordered_wf,
map_wf,
not_wf,
mem_wf,
dset_of_mon_wf,
dset_of_mon_wf0
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
applyEquality,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
productEquality,
independent_functionElimination
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps,qs:|oal(a;b)|. ((\mforall{}u:|a|. ((ps[u]) = (qs[u]))) {}\mRightarrow{} (ps = qs))
Date html generated:
2016_05_16-AM-08_17_19
Last ObjectModification:
2015_12_28-PM-06_27_26
Theory : polynom_2
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