Nuprl Lemma : length-mapfilter
∀[l,f,P:Top]. (||mapfilter(f;P;l)|| ~ ||filter(P;l)||)
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
length: ||as||,
filter: filter(P;l),
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 :
map-length,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[l,f,P:Top]. (||mapfilter(f;P;l)|| \msim{} ||filter(P;l)||)
Date html generated:
2016_05_14-PM-01_29_36
Last ObjectModification:
2015_12_26-PM-05_22_40
Theory : list_1
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