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
Home
Index