Nuprl Lemma : oal_lt_wf
∀s:LOSet. ∀g:OCMon. ∀ps,qs:|oal(s;g)|. (ps << qs ∈ ℙ)
Proof
Definitions occuring in Statement :
oal_lt: ps << qs,
oalist: oal(a;b),
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
ocmon: OCMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
oal_lt: ps << qs,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
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,
so_apply: x[s]
Lemmas referenced :
exists_wf,
set_car_wf,
all_wf,
set_lt_wf,
equal_wf,
grp_car_wf,
lookup_wf,
grp_id_wf,
oalist_wf,
ocmon_subtype_abdmonoid,
dset_wf,
grp_lt_wf,
ocmon_wf,
loset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
lambdaEquality,
productEquality,
functionEquality,
hypothesisEquality,
dependent_functionElimination,
applyEquality
Latex:
\mforall{}s:LOSet. \mforall{}g:OCMon. \mforall{}ps,qs:|oal(s;g)|. (ps << qs \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-10_04_00
Last ObjectModification:
2017_03_03-PM-01_07_08
Theory : polynom_2
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