Nuprl Lemma : finite_set_wf
∀[s:DSet]. (FiniteSet{s} ∈ Type)
Proof
Definitions occuring in Statement :
finite_set: FiniteSet{s},
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
dset: DSet
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
finite_set: FiniteSet{s},
all: ∀x:A. B[x],
dset: DSet,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
mset_wf,
all_wf,
set_car_wf,
le_wf,
mset_count_wf,
nat_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename,
lambdaEquality,
applyEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[s:DSet]. (FiniteSet\{s\} \mmember{} Type)
Date html generated:
2016_05_16-AM-07_46_29
Last ObjectModification:
2015_12_28-PM-06_04_02
Theory : mset
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