Nuprl Lemma : fset_properties
∀s:DSet. ∀a:FiniteSet{s}. {∀x:|s|. ((x #∈ a) ≤ 1)}
Proof
Definitions occuring in Statement :
finite_set: FiniteSet{s},
mset_count: x #∈ a,
guard: {T},
le: A ≤ B,
all: ∀x:A. B[x],
natural_number: $n,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
guard: {T},
all: ∀x:A. B[x],
finite_set: FiniteSet{s},
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
subtype_rel: A ⊆r B,
nat: ℕ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
nat_wf,
mset_count_wf,
sq_stable__le,
dset_wf,
finite_set_wf,
set_car_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
applyEquality,
lambdaEquality,
natural_numberEquality,
independent_functionElimination,
introduction,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}s:DSet. \mforall{}a:FiniteSet\{s\}. \{\mforall{}x:|s|. ((x \#\mmember{} a) \mleq{} 1)\}
Date html generated:
2016_05_16-AM-07_50_56
Last ObjectModification:
2016_01_16-PM-11_39_14
Theory : mset
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