Nuprl Lemma : null-mapfilter
∀P,f,L:Top. (null(mapfilter(f;P;L)) ~ null(filter(P;L)))
Proof
Definitions occuring in Statement :
mapfilter: mapfilter(f;P;L),
null: null(as),
filter: filter(P;l),
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
mapfilter: mapfilter(f;P;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
null-map,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}P,f,L:Top. (null(mapfilter(f;P;L)) \msim{} null(filter(P;L)))
Date html generated:
2016_05_14-PM-01_29_32
Last ObjectModification:
2015_12_26-PM-05_22_29
Theory : list_1
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