Nuprl Lemma : omral_fma_wf2
∀g:OCMon. ∀a:CDRng. (omral_fma(g;a) ∈ FMonAlg(g;a))
Proof
Definitions occuring in Statement :
omral_fma: omral_fma(g;a),
fmonalg: FMonAlg(g;a),
all: ∀x:A. B[x],
member: t ∈ T,
cdrng: CDRng,
ocmon: OCMon
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
fmonalg: FMonAlg(g;a),
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
cdrng: CDRng,
crng: CRng,
rng: Rng,
algebra: algebra{i:l}(A),
module: A-Module,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
monoid_hom: MonHom(M1,M2),
mul_mon_of_rng: r↓xmn,
grp_car: |g|,
pi1: fst(t),
rng_of_alg: a↓rg,
rng_car: |r|,
so_apply: x[s],
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
omral_fma: omral_fma(g;a),
fma_alg: f.alg,
fma_inj: f.inj,
pi2: snd(t),
grp_op: *,
rng_times: *,
omral_alg: omral_alg(g;r),
alg_car: a.car,
alg_times: a.times,
infix_ap: x f y,
grp_id: e,
rng_one: 1,
alg_one: a.one,
omral_one: 11,
uni_sat: a = !x:T. Q[x],
fma_umap: f.umap,
implies: P ⇒ Q,
alg_hom_p: alg_hom_p(a; m; n; f),
algebra_hom: algebra_hom(A; M; N),
module_hom: module_hom(A; M; N),
omralist: omral(g;r),
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,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
add_grp_of_rng: r↓+gp,
tlambda: λx:T. b[x]
Lemmas referenced :
omral_fma_wf,
monoid_hom_wf,
mul_mon_of_rng_wf,
rng_of_alg_wf,
rng_car_wf,
algebra_wf,
monoid_hom_p_wf,
fma_alg_wf,
fma_inj_wf,
all_wf,
uni_sat_wf,
alg_car_wf,
fma_umap_wf,
grp_car_wf,
alg_hom_p_wf,
equal_wf,
compose_wf,
cdrng_wf,
ocmon_wf,
omral_inj_mon_op,
omral_one_wf,
omral_alg_umap_is_hom,
omral_alg_umap_tri_comm,
omral_alg_umap_unique,
module_hom_p_wf,
omral_alg_wf,
fun_thru_2op_wf,
alg_times_wf,
alg_one_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
dependent_set_memberEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
independent_pairFormation,
isectElimination,
setElimination,
rename,
productEquality,
because_Cache,
applyEquality,
sqequalRule,
lambdaEquality,
cumulativity,
universeEquality,
instantiate,
functionEquality,
functionExtensionality,
isect_memberFormation,
isect_memberEquality,
axiomEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
addLevel,
levelHypothesis,
independent_functionElimination
Latex:
\mforall{}g:OCMon. \mforall{}a:CDRng. (omral\_fma(g;a) \mmember{} FMonAlg(g;a))
Date html generated:
2017_10_01-AM-10_07_44
Last ObjectModification:
2017_03_03-PM-01_17_30
Theory : polynom_3
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