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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