Nuprl Lemma : oal_lt_irrefl
∀s:LOSet. ∀g:OCMon. Irrefl(|oal(s;g)|;ps,qs.ps << qs)
Proof
Definitions occuring in Statement :
oal_lt: ps << qs,
oalist: oal(a;b),
irrefl: Irrefl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
ocmon: OCMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
irrefl: Irrefl(T;x,y.E[x; y]),
not: ¬A,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
false: False,
oal_lt: ps << qs,
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
dset: DSet,
guard: {T},
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
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,
uimplies: b supposing a
Lemmas referenced :
oal_lt_wf,
set_car_wf,
oalist_wf,
ocmon_subtype_abdmonoid,
dset_wf,
ocmon_wf,
loset_wf,
grp_lt_irreflexivity,
lookup_wf,
grp_car_wf,
grp_id_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
lambdaEquality,
voidElimination,
isectElimination,
applyEquality,
setElimination,
rename,
because_Cache,
independent_isectElimination
Latex:
\mforall{}s:LOSet. \mforall{}g:OCMon. Irrefl(|oal(s;g)|;ps,qs.ps << qs)
Date html generated:
2016_05_16-AM-08_21_06
Last ObjectModification:
2015_12_28-PM-06_25_09
Theory : polynom_2
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