Nuprl Lemma : oal_hgp_wf2
∀s:LOSet. ∀g:OGrp. (oal_hgp(s;g) ∈ OCMon)
Proof
Definitions occuring in Statement :
oal_hgp: oal_hgp(s;g),
all: ∀x:A. B[x],
member: t ∈ T,
ocgrp: OGrp,
ocmon: OCMon,
loset: LOSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
guard: {T},
exists: ∃x:A. B[x],
ocgrp: OGrp,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
infix_ap: x f y,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
so_lambda: λ2x.t[x],
so_apply: x[s],
oal_hgp: oal_hgp(s;g),
grp_car: |g|,
pi1: fst(t),
oal_grp: oal_grp(s;g),
grp_eq: =b,
pi2: snd(t),
grp_le: ≤b,
mon_hom_inj_p: IsMonHomInj(g;h;f),
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
grp_op: *,
grp_id: e,
inject: Inj(A;B;f),
implies: P ⇒ Q,
oal_merge: ps ++ qs,
hgrp_of_ocgrp: g↓hgrp,
oal_nil: 00,
oalist: oal(a;b),
dset_set: dset_set,
mk_dset: mk_dset(T, eq),
set_eq: =b,
dset_list: s List,
eq_list: as =b bs,
set_prod: s × t,
eq_pair: a =b b,
dset_of_mon: g↓set,
rels_iso: RelsIso(T;T';x,y.R[x; y];x,y.R'[x; y];f),
iff: P ⇐⇒ Q,
dset: DSet,
rev_implies: P ⇐ Q
Lemmas referenced :
inj_into_ocmon,
oal_hgp_wf,
ocgrp_wf,
loset_wf,
hgrp_of_ocgrp_wf2,
ocmon_subtype_abdmonoid,
ocgrp_subtype_ocmon,
subtype_rel_transitivity,
ocmon_wf,
abdmonoid_wf,
oal_grp_wf2,
oal_hgp_subtype_oal_grp,
grp_car_wf,
mon_hom_inj_p_wf,
oal_grp_wf,
ocgrp_subtype_abdgrp,
rels_iso_wf,
assert_wf,
infix_ap_wf,
bool_wf,
grp_eq_wf,
grp_le_wf,
exists_wf,
equal_wf,
oal_merge_wf2,
set_car_inc,
oal_nil_wf,
oalist_hgrp_eqs,
set_eq_wf,
oalist_wf,
dset_wf,
set_car_wf,
oal_ble_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_isectElimination,
applyEquality,
sqequalRule,
independent_pairFormation,
instantiate,
dependent_pairFormation,
productElimination,
lambdaEquality,
setElimination,
rename,
because_Cache,
productEquality,
functionEquality,
isect_memberFormation,
introduction,
isect_memberEquality,
axiomEquality,
independent_functionElimination
Latex:
\mforall{}s:LOSet. \mforall{}g:OGrp. (oal\_hgp(s;g) \mmember{} OCMon)
Date html generated:
2016_05_16-AM-08_22_34
Last ObjectModification:
2015_12_28-PM-06_28_06
Theory : polynom_2
Home
Index