Nuprl Lemma : mapfilter-append
∀[as,bs,P,f:Top]. (mapfilter(f;P;as @ bs) ~ mapfilter(f;P;as) @ mapfilter(f;P;bs))
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
append: as @ bs,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mapfilter: mapfilter(f;P;L),
top: Top
Lemmas referenced :
filter_append_sq,
map_append_sq,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[as,bs,P,f:Top]. (mapfilter(f;P;as @ bs) \msim{} mapfilter(f;P;as) @ mapfilter(f;P;bs))
Date html generated:
2016_05_14-PM-01_28_44
Last ObjectModification:
2015_12_26-PM-05_21_35
Theory : list_1
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