Nuprl Lemma : bag-map-mapfilter
∀[b,P,f,g:Top]. (bag-map(g;bag-mapfilter(f;P;b)) ~ bag-mapfilter(g o f;P;b))
Proof
Definitions occuring in Statement :
bag-mapfilter: bag-mapfilter(f;P;bs),
bag-map: bag-map(f;bs),
compose: f o g,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-mapfilter: bag-mapfilter(f;P;bs),
top: Top
Lemmas referenced :
bag-map-map,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[b,P,f,g:Top]. (bag-map(g;bag-mapfilter(f;P;b)) \msim{} bag-mapfilter(g o f;P;b))
Date html generated:
2016_05_15-PM-02_25_59
Last ObjectModification:
2015_12_27-AM-09_52_23
Theory : bags
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