Nuprl Lemma : dist_hom_over_mset_for
∀s:DSet. ∀m,n:IAbMonoid. ∀f:MonHom(m,n). ∀a:MSet{s}. ∀g:|s| ⟶ |m|.
((f (msFor{m} x ∈ a. g[x])) = (msFor{n} x ∈ a. (f g[x])) ∈ |n|)
Proof
Definitions occuring in Statement :
mset_for: mset_for,
mset: MSet{s},
so_apply: x[s],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T,
monoid_hom: MonHom(M1,M2),
iabmonoid: IAbMonoid,
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],
iabmonoid: IAbMonoid,
imon: IMonoid,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
dset: DSet,
monoid_hom: MonHom(M1,M2),
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
monoid_hom_wf,
iabmonoid_wf,
dset_wf,
mset_for_elim_lemma,
all_mset_elim,
all_wf,
set_car_wf,
grp_car_wf,
equal_wf,
mset_for_wf,
mset_wf,
sq_stable__all,
sq_stable__equal,
list_wf,
mon_for_wf,
dist_hom_over_mon_for
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
addLevel,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality,
functionEquality,
applyEquality,
because_Cache,
independent_functionElimination,
productElimination,
levelHypothesis
Latex:
\mforall{}s:DSet. \mforall{}m,n:IAbMonoid. \mforall{}f:MonHom(m,n). \mforall{}a:MSet\{s\}. \mforall{}g:|s| {}\mrightarrow{} |m|.
((f (msFor\{m\} x \mmember{} a. g[x])) = (msFor\{n\} x \mmember{} a. (f g[x])))
Date html generated:
2016_05_16-AM-07_47_55
Last ObjectModification:
2015_12_28-PM-06_03_21
Theory : mset
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