Nuprl Lemma : mset_map_char
∀s,s':DSet. ∀f:|s| ⟶ |s'|. ∀as:|s| List. (msmap{s,s'}(f;mk_mset(as)) = mk_mset(map(f;as)) ∈ MSet{s'})
Proof
Definitions occuring in Statement :
mset_map: msmap{s,s'}(f;a),
mk_mset: mk_mset(as),
mset: MSet{s},
map: map(f;as),
list: T List,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
equal: s = t ∈ T,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
top: Top,
prop: ℙ,
mk_mset: mk_mset(as),
null_mset: 0{s},
mset_map: msmap{s,s'}(f;a),
mset_mon: mset_mon{s},
grp_id: e,
pi2: snd(t),
pi1: fst(t),
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
grp_op: *,
infix_ap: x f y
Lemmas referenced :
list_induction,
set_car_wf,
equal_wf,
mset_wf,
mset_map_wf,
mk_mset_wf,
map_wf,
list_wf,
map_nil_lemma,
map_cons_lemma,
dset_wf,
mset_for_null_lemma,
null_mset_wf,
squash_wf,
true_wf,
mk_mset_cons,
iff_weakening_equal,
mset_for_inj_lemma,
mset_sum_wf,
mset_inj_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
functionExtensionality,
applyEquality,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
functionEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination
Latex:
\mforall{}s,s':DSet. \mforall{}f:|s| {}\mrightarrow{} |s'|. \mforall{}as:|s| List. (msmap\{s,s'\}(f;mk\_mset(as)) = mk\_mset(map(f;as)))
Date html generated:
2017_10_01-AM-09_59_42
Last ObjectModification:
2017_03_03-PM-01_00_52
Theory : mset
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