Nuprl Lemma : mcopower_umap_comm_tri_a
∀s:DSet. ∀g:AbMon. ∀c:MCopower(s;g). ∀h:AbMon. ∀f:|s| ⟶ MonHom(g,h). ∀a:|g|. ∀j:|s|.
((f j a) = (c.umap h f (c.inj j a)) ∈ |h|)
Proof
Definitions occuring in Statement :
mcopower: MCopower(s;g),
mcopower_umap: m.umap,
mcopower_inj: m.inj,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T,
monoid_hom: MonHom(M1,M2),
abmonoid: AbMon,
grp_car: |g|,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
abmonoid: AbMon,
mon: Mon,
compose: f o g,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
monoid_hom: MonHom(M1,M2),
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
set_car_wf,
grp_car_wf,
monoid_hom_wf,
abmonoid_wf,
mcopower_wf,
dset_wf,
equal_wf,
squash_wf,
true_wf,
mcopower_umap_comm_tri,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
functionEquality,
dependent_functionElimination,
sqequalRule,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
functionExtensionality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
because_Cache
Latex:
\mforall{}s:DSet. \mforall{}g:AbMon. \mforall{}c:MCopower(s;g). \mforall{}h:AbMon. \mforall{}f:|s| {}\mrightarrow{} MonHom(g,h). \mforall{}a:|g|. \mforall{}j:|s|.
((f j a) = (c.umap h f (c.inj j a)))
Date html generated:
2017_10_01-AM-10_01_15
Last ObjectModification:
2017_03_03-PM-01_03_29
Theory : polynom_1
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