Nuprl Lemma : mk_mset_wf2
∀s:DSet. ∀as:DisList{s}. (mk_mset(as) ∈ FiniteSet{s})
Proof
Definitions occuring in Statement :
finite_set: FiniteSet{s},
mk_mset: mk_mset(as),
dislist: DisList{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
guard: {T},
finite_set: FiniteSet{s},
dislist: DisList{s},
uall: ∀[x:A]. B[x],
dset: DSet,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
prop: ℙ,
mk_mset: mk_mset(as),
mset_count: x #∈ a
Lemmas referenced :
dislist_properties,
mk_mset_wf,
set_car_wf,
all_wf,
le_wf,
mset_count_wf,
nat_wf,
dislist_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
setElimination,
rename,
isectElimination,
sqequalRule,
lambdaEquality,
applyEquality,
natural_numberEquality
Latex:
\mforall{}s:DSet. \mforall{}as:DisList\{s\}. (mk\_mset(as) \mmember{} FiniteSet\{s\})
Date html generated:
2016_05_16-AM-07_46_31
Last ObjectModification:
2015_12_28-PM-06_03_56
Theory : mset
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