Nuprl Lemma : oalist_wf
∀a:LOSet. ∀b:AbDMon. (oal(a;b) ∈ DSet)
Proof
Definitions occuring in Statement :
oalist: oal(a;b),
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
oalist: oal(a;b),
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
dset: DSet,
set_prod: s × t,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
dset_list: s List,
dset_of_mon: g↓set,
pi2: snd(t),
so_apply: x[s]
Lemmas referenced :
abdmonoid_properties,
dmon_properties,
dset_set_wf,
dset_list_wf,
set_prod_wf,
dset_of_mon_wf,
abdmonoid_wf,
assert_wf,
sd_ordered_wf,
map_wf,
set_car_wf,
not_wf,
mem_wf,
grp_id_wf,
grp_car_wf,
dset_of_mon_wf0,
dset_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
applyEquality,
lambdaEquality,
sqequalRule,
productEquality,
because_Cache,
productElimination
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. (oal(a;b) \mmember{} DSet)
Date html generated:
2016_05_16-AM-08_15_23
Last ObjectModification:
2015_12_28-PM-06_28_39
Theory : polynom_2
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