Nuprl Lemma : no-repeats-bag-to-set
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. bag-no-repeats(T;bag-to-set(eq;bs))
Proof
Definitions occuring in Statement :
bag-to-set: bag-to-set(eq;bs),
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-to-set: bag-to-set(eq;bs),
bag-no-repeats: bag-no-repeats(T;bs),
squash: ↓T
Lemmas referenced :
deq_wf,
bag_wf,
bag-remove-repeats-no-repeats
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. bag-no-repeats(T;bag-to-set(eq;bs))
Date html generated:
2016_05_15-PM-08_03_04
Last ObjectModification:
2016_01_16-PM-01_29_51
Theory : bags_2
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