Nuprl Lemma : mcopower_umap_is_hom
∀s:DSet. ∀g:AbMon. ∀c:MCopower(s;g). ∀h:AbMon. ∀f:|s| ⟶ MonHom(g,h). IsMonHom{c.mon,h}(c.umap h f)
Proof
Definitions occuring in Statement :
mcopower: MCopower(s;g),
mcopower_umap: m.umap,
mcopower_mon: m.mon,
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
monoid_hom: MonHom(M1,M2),
monoid_hom_p: IsMonHom{M1,M2}(f),
abmonoid: AbMon,
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,
functionEquality,
isectElimination,
setElimination,
rename
Latex:
\mforall{}s:DSet. \mforall{}g:AbMon. \mforall{}c:MCopower(s;g). \mforall{}h:AbMon. \mforall{}f:|s| {}\mrightarrow{} MonHom(g,h). IsMonHom\{c.mon,h\}(c.umap h f)
Date html generated:
2016_05_16-AM-08_13_07
Last ObjectModification:
2015_12_28-PM-06_09_53
Theory : polynom_1
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