Nuprl Lemma : oal_omcp_wf
∀s:LOSet. ∀g:OGrp. (oal_omcp{s,g} ∈ MCopower(s;g↓hgrp))
Proof
Definitions occuring in Statement :
oal_omcp: oal_omcp{s,g},
mcopower: MCopower(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
hgrp_of_ocgrp: g↓hgrp,
ocgrp: OGrp,
loset: LOSet
Definitions unfolded in proof :
oal_omcp: oal_omcp{s,g},
all: ∀x:A. B[x],
member: t ∈ T,
mcopower: MCopower(s;g),
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
prop: ℙ,
mcopower_sig: mcopower_sig{i:l}(s;g),
guard: {T},
loset: LOSet,
poset: POSet{i},
qoset: QOSet,
dset: DSet,
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,
hgrp_of_ocgrp: g↓hgrp,
grp_id: e,
pi2: snd(t),
grp_car: |g|,
oal_hgp: oal_hgp(s;g),
and: P ∧ Q,
cand: A c∧ B,
mcopower_mon: m.mon,
mcopower_inj: m.inj,
monoid_hom_p: IsMonHom{M1,M2}(f),
oal_mon: oal_mon(a;b),
grp_op: *,
mcopower_umap: m.umap,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
monoid_hom: MonHom(M1,M2)
Lemmas referenced :
ocgrp_wf,
loset_wf,
hgrp_of_ocgrp_wf2,
ocmon_wf,
abmonoid_properties,
mon_wf,
comm_wf,
grp_car_wf,
grp_op_wf,
oal_hgp_wf2,
oal_inj_wf,
ocmon_subtype_abdmonoid,
set_car_wf,
oal_umap_wf,
oalist_wf,
dset_wf,
abmonoid_wf,
oal_hgp_wf,
monoid_hom_wf,
hgrp_of_ocgrp_wf,
oal_inj_mon_hom,
oal_umap_char_a,
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,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
setEquality,
cumulativity,
dependent_pairEquality,
dependent_functionElimination,
because_Cache,
functionEquality,
universeEquality,
productEquality,
independent_pairFormation,
instantiate,
independent_isectElimination
Latex:
\mforall{}s:LOSet. \mforall{}g:OGrp. (oal\_omcp\{s,g\} \mmember{} MCopower(s;g\mdownarrow{}hgrp))
Date html generated:
2016_05_16-AM-08_23_14
Last ObjectModification:
2015_12_28-PM-06_26_18
Theory : polynom_2
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