Nuprl Lemma : fset_of_mset_wf
∀s:DSet. ∀a:MSet{s}. (fset_of_mset(s;a) ∈ MSet{s})
Proof
Definitions occuring in Statement :
fset_of_mset: fset_of_mset(s;a),
mset: MSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
fset_of_mset: fset_of_mset(s;a),
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
mset_union_mon: <MSet{s},⋃,0>,
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_union_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
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. (fset\_of\_mset(s;a) \mmember{} MSet\{s\})
Date html generated:
2016_05_16-AM-07_50_12
Last ObjectModification:
2015_12_28-PM-06_01_03
Theory : mset
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