Nuprl Lemma : nil_in_oalist
∀a:LOSet. ∀b:AbDMon. ([] ∈ |oal(a;b)|)
Proof
Definitions occuring in Statement :
oalist: oal(a;b),
nil: [],
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
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,
uall: ∀[x:A]. B[x],
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
and: P ∧ Q,
cand: A c∧ B,
true: True,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
pi2: snd(t)
Lemmas referenced :
abdmonoid_wf,
loset_wf,
nil_wf,
set_car_wf,
grp_car_wf,
map_nil_lemma,
istype-void,
sd_ordered_nil_lemma,
mem_nil_lemma,
assert_wf,
sd_ordered_wf,
map_wf,
not_wf,
mem_wf,
dset_of_mon_wf,
grp_id_wf,
dset_of_mon_wf0
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
sqequalRule,
dependent_set_memberEquality_alt,
isectElimination,
thin,
productEquality,
setElimination,
rename,
hypothesisEquality,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
natural_numberEquality,
independent_pairFormation,
productIsType,
because_Cache,
lambdaEquality_alt,
productElimination,
applyEquality
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. ([] \mmember{} |oal(a;b)|)
Date html generated:
2019_10_16-PM-01_07_07
Last ObjectModification:
2018_10_08-PM-00_17_43
Theory : polynom_2
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