Nuprl Lemma : oal_nil_ident_r
∀a:LOSet. ∀b:AbDMon. ∀ps:|oal(a;b)|. ((ps ++ 00) = ps ∈ |oal(a;b)|)
Proof
Definitions occuring in Statement :
oal_merge: ps ++ qs,
oal_nil: 00,
oalist: oal(a;b),
all: ∀x:A. B[x],
equal: s = t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
so_apply: x[s],
implies: P ⇒ Q,
oal_nil: 00,
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,
top: Top,
prop: ℙ,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
guard: {T}
Lemmas referenced :
oalist_cases_a,
equal_wf,
set_car_wf,
oalist_wf,
dset_wf,
oal_merge_wf2,
oal_nil_wf,
oal_merge_left_nil_lemma,
nil_in_oalist,
oal_merge_right_nil_lemma,
cons_in_oalist,
not_wf,
grp_car_wf,
grp_id_wf,
assert_wf,
before_wf,
map_wf,
set_prod_wf,
dset_of_mon_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
isectElimination,
hypothesis,
applyEquality,
setElimination,
rename,
because_Cache,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps:|oal(a;b)|. ((ps ++ 00) = ps)
Date html generated:
2016_05_16-AM-08_18_21
Last ObjectModification:
2015_12_28-PM-06_26_58
Theory : polynom_2
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