Nuprl Lemma : mset_for_mset_inj
∀s:DSet. ∀g:IAbMonoid. ∀f:|s| ⟶ |g|. ∀u:|s|. ((msFor{g} x ∈ mset_inj{s}(u). f[x]) = f[u] ∈ |g|)
Proof
Definitions occuring in Statement :
mset_for: mset_for,
mset_inj: mset_inj{s}(x),
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T,
iabmonoid: IAbMonoid,
grp_car: |g|,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
mset_inj: mset_inj{s}(x),
mset_for: mset_for,
mk_mset: mk_mset(as),
so_lambda: λ2x.t[x],
member: t ∈ T,
top: Top,
so_apply: x[s],
uall: ∀[x:A]. B[x],
dset: DSet,
iabmonoid: IAbMonoid,
imon: IMonoid,
squash: ↓T,
prop: ℙ,
and: P ∧ Q,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
mon_for_cons_lemma,
mon_for_nil_lemma,
set_car_wf,
grp_car_wf,
iabmonoid_wf,
dset_wf,
equal_wf,
squash_wf,
true_wf,
mon_ident,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
setElimination,
rename,
hypothesisEquality,
functionEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
functionExtensionality,
productElimination,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}s:DSet. \mforall{}g:IAbMonoid. \mforall{}f:|s| {}\mrightarrow{} |g|. \mforall{}u:|s|. ((msFor\{g\} x \mmember{} mset\_inj\{s\}(u). f[x]) = f[u])
Date html generated:
2017_10_01-AM-09_59_21
Last ObjectModification:
2017_03_03-PM-01_00_13
Theory : mset
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