Nuprl Lemma : fmonalg_wf
∀g:AbMon. ∀a:CRng. (FMonAlg(g;a) ∈ 𝕌')
Proof
Definitions occuring in Statement :
fmonalg: FMonAlg(g;a),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type,
crng: CRng,
abmonoid: AbMon
Definitions unfolded in proof :
fmonalg: FMonAlg(g;a),
all: ∀x:A. B[x],
member: t ∈ T,
abmonoid: AbMon,
mon: Mon,
crng: CRng,
rng: Rng,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
algebra: algebra{i:l}(A),
module: A-Module,
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]
Lemmas referenced :
fma_sig_wf,
monoid_hom_p_wf,
mul_mon_of_rng_wf,
rng_of_alg_wf,
rng_car_wf,
fma_alg_wf,
fma_inj_wf,
all_wf,
algebra_wf,
monoid_hom_wf,
uni_sat_wf,
alg_car_wf,
fma_umap_wf,
grp_car_wf,
alg_hom_p_wf,
equal_wf,
compose_wf,
crng_wf,
abmonoid_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
setEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
because_Cache,
hypothesis,
productEquality,
cumulativity,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
lambdaEquality,
functionEquality,
functionExtensionality
Latex:
\mforall{}g:AbMon. \mforall{}a:CRng. (FMonAlg(g;a) \mmember{} \mBbbU{}')
Date html generated:
2017_10_01-AM-10_01_22
Last ObjectModification:
2017_03_03-PM-01_03_52
Theory : polynom_1
Home
Index