Nuprl Lemma : oal_lv_nid
∀s:LOSet. ∀g:AbDMon. ∀ps:|oal(s;g)|. ((¬(ps = 00 ∈ |oal(s;g)|)) ⇒ (¬(lv(ps) = e ∈ |g|)))
Proof
Definitions occuring in Statement :
oal_lv: lv(ps),
oal_nil: 00,
oalist: oal(a;b),
all: ∀x:A. B[x],
not: ¬A,
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],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
dset: DSet,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
so_apply: x[s],
guard: {T},
false: False,
not: ¬A,
oal_nil: 00,
oal_lv: lv(ps),
top: Top,
pi2: snd(t),
oal_cons_pr: oal_cons_pr(x;y;ws),
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
set_prod: s × t,
mk_dset: mk_dset(T, eq),
set_car: |p|,
pi1: fst(t),
oalist: oal(a;b),
dset_set: dset_set,
dset_list: s List,
dset_of_mon: g↓set
Lemmas referenced :
oalist_cases_a,
not_wf,
equal_wf,
set_car_wf,
oalist_wf,
dset_wf,
oal_nil_wf,
grp_car_wf,
oal_lv_wf,
grp_id_wf,
abdmonoid_wf,
loset_wf,
reduce_hd_cons_lemma,
oal_cons_pr_wf,
assert_wf,
before_wf,
map_wf,
set_prod_wf,
dset_of_mon_wf,
pi1_wf_top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
functionEquality,
isectElimination,
hypothesis,
applyEquality,
setElimination,
rename,
independent_functionElimination,
because_Cache,
voidElimination,
lemma_by_obid,
isect_memberEquality,
voidEquality,
productElimination,
independent_pairEquality
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDMon. \mforall{}ps:|oal(s;g)|. ((\mneg{}(ps = 00)) {}\mRightarrow{} (\mneg{}(lv(ps) = e)))
Date html generated:
2019_10_16-PM-01_08_02
Last ObjectModification:
2018_08_22-AM-11_44_37
Theory : polynom_2
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