Nuprl Lemma : fset_of_mset_wf2
∀s:DSet. ∀a:MSet{s}. (fset_of_mset(s;a) ∈ FiniteSet{s})
Proof
Definitions occuring in Statement :
fset_of_mset: fset_of_mset(s;a),
finite_set: FiniteSet{s},
mset: MSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
finite_set: FiniteSet{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
Lemmas referenced :
fset_of_mset_wf,
fset_of_mset_count_bound,
set_car_wf,
all_wf,
le_wf,
mset_count_wf,
nat_wf,
mset_wf,
dset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
dependent_set_memberEquality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
setElimination,
rename,
sqequalRule,
lambdaEquality,
applyEquality,
natural_numberEquality
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. (fset\_of\_mset(s;a) \mmember{} FiniteSet\{s\})
Date html generated:
2016_05_16-AM-07_50_19
Last ObjectModification:
2015_12_28-PM-06_00_49
Theory : mset
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