Nuprl Lemma : count-bag-to-set
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. ∀[x:T]. ((#x in bag-to-set(eq;bs)) ~ if 0 <z (#x in bs) then 1 else 0 fi )
Proof
Definitions occuring in Statement :
bag-to-set: bag-to-set(eq;bs),
bag-count: (#x in bs),
bag: bag(T),
deq: EqDecider(T),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
bag-to-set: bag-to-set(eq;bs)
Lemmas referenced :
count-bag-remove-repeats
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. \mforall{}[x:T].
((\#x in bag-to-set(eq;bs)) \msim{} if 0 <z (\#x in bs) then 1 else 0 fi )
Date html generated:
2016_05_15-PM-08_03_01
Last ObjectModification:
2015_12_27-PM-04_15_31
Theory : bags_2
Home
Index