Nuprl Lemma : null-bag-mapfilter
∀P,f,bs:Top. (bag-null(bag-mapfilter(f;P;bs)) ~ bag-null([x∈bs|P x]))
Proof
Definitions occuring in Statement :
bag-null: bag-null(bs),
bag-mapfilter: bag-mapfilter(f;P;bs),
bag-filter: [x∈b|p[x]],
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
bag-null: bag-null(bs)
Lemmas referenced :
bag-mapfilter-null
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis
Latex:
\mforall{}P,f,bs:Top. (bag-null(bag-mapfilter(f;P;bs)) \msim{} bag-null([x\mmember{}bs|P x]))
Date html generated:
2016_05_15-PM-02_24_25
Last ObjectModification:
2015_12_27-AM-09_53_29
Theory : bags
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