Nuprl Lemma : bag-count-append
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:bag(T)]. ∀[x:T]. ((#x in as + bs) = ((#x in as) + (#x in bs)) ∈ ℤ)
Proof
Definitions occuring in Statement :
bag-count: (#x in bs),
bag-append: as + bs,
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
add: n + m,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
deq: EqDecider(T),
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
bag_wf,
deq_wf,
bag-append_wf,
bag-filter-append,
bag-size-append,
bag-size_wf,
assert_wf,
bag-filter_wf,
bag-count-sqequal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
hypothesisEquality,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
because_Cache,
lemma_by_obid,
universeEquality,
voidElimination,
voidEquality,
addEquality,
setEquality,
cumulativity,
applyEquality,
setElimination,
rename,
lambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:bag(T)]. \mforall{}[x:T].
((\#x in as + bs) = ((\#x in as) + (\#x in bs)))
Date html generated:
2016_05_15-PM-07_57_53
Last ObjectModification:
2015_12_27-PM-04_17_07
Theory : bags_2
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