Nuprl Lemma : oal_null_wf
∀s:LOSet. ∀g:AbDMon. ∀ps:|oal(s;g)|. (null(ps) ∈ 𝔹)
Proof
Definitions occuring in Statement :
oal_null: null(ps),
oalist: oal(a;b),
bool: 𝔹,
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
oal_null: null(ps),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
abdmonoid: AbDMon,
subtype_rel: A ⊆r B,
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,
dset: DSet
Lemmas referenced :
null_wf,
set_car_wf,
set_prod_wf,
dset_of_mon_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
lambdaEquality,
dependent_functionElimination
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDMon. \mforall{}ps:|oal(s;g)|. (null(ps) \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-08_19_32
Last ObjectModification:
2015_12_28-PM-06_25_56
Theory : polynom_2
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