Nuprl Lemma : bag-mapfilter-fast-map
∀[bs:bag(Top)]. ∀[P,f,g:Top]. (bag-mapfilter-fast(f;P;bag-map(g;bs)) ~ bag-mapfilter-fast(f o g;P o g;bs))
Proof
Definitions occuring in Statement :
bag-mapfilter-fast: bag-mapfilter-fast(f;P;bs),
bag-map: bag-map(f;bs),
bag: bag(T),
compose: f o g,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
bag-mapfilter-fast: bag-mapfilter-fast(f;P;bs),
bag-map: bag-map(f;bs),
bag-accum: bag-accum(v,x.f[v; x];init;bs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
compose: f o g,
so_apply: x[s]
Lemmas referenced :
list_accum-map,
top_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[bs:bag(Top)]. \mforall{}[P,f,g:Top].
(bag-mapfilter-fast(f;P;bag-map(g;bs)) \msim{} bag-mapfilter-fast(f o g;P o g;bs))
Date html generated:
2016_05_15-PM-02_50_20
Last ObjectModification:
2015_12_27-AM-09_34_34
Theory : bags
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