Nuprl Lemma : dislist_properties
∀s:DSet. ∀as:DisList{s}. {∀x:|s|. ((x #∈ as) ≤ 1)}
Proof
Definitions occuring in Statement :
dislist: DisList{s},
count: a #∈ as,
guard: {T},
le: A ≤ B,
all: ∀x:A. B[x],
natural_number: $n,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
guard: {T},
dislist: DisList{s},
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
sq_stable: SqStable(P),
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
prop: ℙ,
squash: ↓T
Lemmas referenced :
dset_wf,
dislist_wf,
squash_wf,
less_than'_wf,
sq_stable__le,
count_wf,
le_wf,
set_car_wf,
sq_stable__all
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
natural_numberEquality,
independent_functionElimination,
introduction,
productElimination,
independent_pairEquality,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}s:DSet. \mforall{}as:DisList\{s\}. \{\mforall{}x:|s|. ((x \#\mmember{} as) \mleq{} 1)\}
Date html generated:
2016_05_16-AM-07_39_57
Last ObjectModification:
2016_01_16-PM-11_12_16
Theory : list_2
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