Nuprl Lemma : mset_map_wf
∀s,s':DSet. ∀f:|s| ⟶ |s'|. ∀a:MSet{s}. (msmap{s,s'}(f;a) ∈ MSet{s'})
Proof
Definitions occuring in Statement :
mset_map: msmap{s,s'}(f;a),
mset: MSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
mset_map: msmap{s,s'}(f;a),
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
mset_mon: mset_mon{s},
grp_car: |g|,
pi1: fst(t),
uall: ∀[x:A]. B[x],
dset: DSet,
so_apply: x[s],
abmonoid: AbMon,
mon: Mon
Lemmas referenced :
mset_for_wf,
mset_mon_wf,
abmonoid_subtype_iabmonoid,
mset_inj_wf,
mset_wf,
set_car_wf,
grp_car_wf,
abmonoid_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
isectElimination,
setElimination,
rename,
functionEquality
Latex:
\mforall{}s,s':DSet. \mforall{}f:|s| {}\mrightarrow{} |s'|. \mforall{}a:MSet\{s\}. (msmap\{s,s'\}(f;a) \mmember{} MSet\{s'\})
Date html generated:
2016_05_16-AM-07_48_41
Last ObjectModification:
2015_12_28-PM-06_02_30
Theory : mset
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