Nuprl Lemma : mcopower_umap_comm_tri
∀s:DSet. ∀g:AbMon. ∀c:MCopower(s;g). ∀h:AbMon. ∀f:|s| ⟶ MonHom(g,h). ∀j:|s|.
((f j) = ((c.umap h f) o (c.inj j)) ∈ (|g| ⟶ |h|))
Proof
Definitions occuring in Statement :
mcopower: MCopower(s;g),
mcopower_umap: m.umap,
mcopower_inj: m.inj,
compose: f o g,
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],
uni_sat: a = !x:T. Q[x],
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
dset: DSet,
abmonoid: AbMon,
mon: Mon
Lemmas referenced :
mcopower_properties,
set_car_wf,
monoid_hom_wf,
abmonoid_wf,
mcopower_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
isectElimination,
setElimination,
rename,
functionEquality
Latex:
\mforall{}s:DSet. \mforall{}g:AbMon. \mforall{}c:MCopower(s;g). \mforall{}h:AbMon. \mforall{}f:|s| {}\mrightarrow{} MonHom(g,h). \mforall{}j:|s|.
((f j) = ((c.umap h f) o (c.inj j)))
Date html generated:
2016_05_16-AM-08_13_08
Last ObjectModification:
2015_12_28-PM-06_09_52
Theory : polynom_1
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