Nuprl Lemma : bag-mapfilter-append
∀[T:Type]. ∀[a:bag(T)]. ∀[b:bag(Top)]. ∀[f:Top]. ∀[P:T ⟶ 𝔹].
(bag-mapfilter(f;P;a + b) ~ bag-mapfilter(f;P;a) + bag-mapfilter(f;P;b))
Proof
Definitions occuring in Statement :
bag-mapfilter: bag-mapfilter(f;P;bs),
bag-append: as + bs,
bag: bag(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-mapfilter: bag-mapfilter(f;P;bs),
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
bag-filter-append,
bag-map-append,
bag-filter_wf,
subtype_rel_bag,
top_wf,
assert_wf,
bool_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
lambdaEquality,
applyEquality,
setEquality,
independent_isectElimination,
because_Cache,
sqequalAxiom,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:bag(T)]. \mforall{}[b:bag(Top)]. \mforall{}[f:Top]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}].
(bag-mapfilter(f;P;a + b) \msim{} bag-mapfilter(f;P;a) + bag-mapfilter(f;P;b))
Date html generated:
2016_05_15-PM-02_25_55
Last ObjectModification:
2015_12_27-AM-09_52_40
Theory : bags
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