Nuprl Lemma : assert_of_oal_null
∀s:LOSet. ∀g:AbDMon. ∀ps:|oal(s;g)|. (↑null(ps) ⇐⇒ ps = 00 ∈ |oal(s;g)|)
Proof
Definitions occuring in Statement :
oal_null: null(ps),
oal_nil: 00,
oalist: oal(a;b),
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
equal: s = t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
uimplies: b supposing a,
uiff: uiff(P;Q),
dset_of_mon: g↓set,
set_prod: s × t,
dset_list: s List,
pi1: fst(t),
set_car: |p|,
mk_dset: mk_dset(T, eq),
dset_set: dset_set,
oalist: oal(a;b),
dset: DSet,
subtype_rel: A ⊆r B,
abdmonoid: AbDMon,
qoset: QOSet,
poset: POSet{i},
loset: LOSet,
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
iff: P ⇐⇒ Q,
oal_null: null(ps),
all: ∀x:A. B[x],
pi2: snd(t),
mon: Mon,
dmon: DMon,
cand: A c∧ B,
oal_nil: 00
Lemmas referenced :
oalist_car_properties,
sd_ordered_wf,
map_wf,
grp_car_wf,
not_wf,
mem_wf,
grp_id_wf,
dset_of_mon_wf0,
assert_of_null,
set_car_wf,
set_prod_wf,
dset_of_mon_wf,
dset_wf,
oalist_wf,
assert_wf,
null_wf,
iff_wf,
equal-wf-T-base,
list_wf,
equal_wf,
oal_nil_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
baseClosed,
equalitySymmetry,
equalityTransitivity,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
hypothesisEquality,
rename,
setElimination,
isectElimination,
lemma_by_obid,
impliesFunctionality,
independent_pairFormation,
thin,
productElimination,
sqequalHypSubstitution,
addLevel,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productEquality,
dependent_set_memberEquality
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDMon. \mforall{}ps:|oal(s;g)|. (\muparrow{}null(ps) \mLeftarrow{}{}\mRightarrow{} ps = 00)
Date html generated:
2016_05_16-AM-08_19_34
Last ObjectModification:
2016_01_16-PM-11_56_45
Theory : polynom_2
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