Nuprl Lemma : oal_mcp_wf
∀s:LOSet. ∀g:AbDMon. (oal_mcp(s;g) ∈ MCopower(s;g))
Proof
Definitions occuring in Statement :
oal_mcp: oal_mcp(s;g),
mcopower: MCopower(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet
Definitions unfolded in proof :
oal_mcp: oal_mcp(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
mcopower: MCopower(s;g),
mcopower_sig: mcopower_sig{i:l}(s;g),
subtype_rel: A ⊆r B,
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
abdmonoid: AbDMon,
dmon: DMon,
mon: Mon,
oal_mon: oal_mon(a;b),
grp_car: |g|,
pi1: fst(t),
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
set_car: |p|,
dset_list: s List,
set_prod: s × t,
dset_of_mon: g↓set,
so_apply: x[s],
abmonoid: AbMon,
and: P ∧ Q,
cand: A c∧ B,
mcopower_mon: m.mon,
mcopower_inj: m.inj,
pi2: snd(t),
dset: DSet,
mcopower_umap: m.umap,
tlambda: λx:T. b[x],
prop: ℙ,
uimplies: b supposing a,
monoid_hom: MonHom(M1,M2)
Lemmas referenced :
abdmonoid_wf,
loset_wf,
oal_mon_wf,
abdmonoid_abmonoid,
oal_inj_wf,
mset_for_wf,
abmonoid_subtype_iabmonoid,
lookup_wf,
grp_car_wf,
grp_id_wf,
oal_dom_wf,
abmonoid_wf,
set_car_wf,
oal_inj_mon_hom,
oal_umap_char,
monoid_hom_wf,
all_wf,
monoid_hom_p_wf,
mcopower_mon_wf,
mcopower_inj_wf,
uni_sat_wf,
mcopower_umap_wf,
subtype_rel_dep_function,
equal_wf,
compose_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
lemma_by_obid,
dependent_set_memberEquality,
dependent_pairEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
because_Cache,
setElimination,
rename,
isectElimination,
functionEquality,
cumulativity,
universeEquality,
productEquality,
independent_pairFormation,
instantiate,
independent_isectElimination
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDMon. (oal\_mcp(s;g) \mmember{} MCopower(s;g))
Date html generated:
2016_05_16-AM-08_23_05
Last ObjectModification:
2015_12_28-PM-06_28_57
Theory : polynom_2
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