Nuprl Lemma : oal_nil_wf
∀a:LOSet. ∀b:AbDMon. (00 ∈ |oal(a;b)|)
Proof
Definitions occuring in Statement :
oal_nil: 00,
oalist: oal(a;b),
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
oal_nil: 00,
all: ∀x:A. B[x],
member: t ∈ T,
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,
and: P ∧ Q,
cand: A c∧ B,
assert: ↑b,
ifthenelse: if b then t else f fi ,
sd_ordered: sd_ordered(as),
ycomb: Y,
list_ind: list_ind,
map: map(f;as),
nil: [],
it: ⋅,
btrue: tt,
true: True,
not: ¬A,
implies: P ⇒ Q,
false: False,
mem: a ∈b as,
mon_for: For{g} x ∈ as. f[x],
for: For{T,op,id} x ∈ as. f[x],
reduce: reduce(f;k;as),
grp_id: e,
pi2: snd(t),
bor_mon: <𝔹,∨b>,
bfalse: ff,
prop: ℙ,
uall: ∀[x:A]. B[x],
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
subtype_rel: A ⊆r B,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet
Lemmas referenced :
assert_wf,
mem_wf,
dset_of_mon_wf,
grp_id_wf,
nil_wf,
set_car_wf,
dset_of_mon_wf0,
grp_car_wf,
sd_ordered_wf,
map_wf,
not_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
hypothesis,
natural_numberEquality,
independent_pairFormation,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
applyEquality,
because_Cache,
dependent_set_memberEquality,
productEquality,
productElimination,
lambdaEquality
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. (00 \mmember{} |oal(a;b)|)
Date html generated:
2016_05_16-AM-08_15_49
Last ObjectModification:
2015_12_28-PM-06_28_40
Theory : polynom_2
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