Nuprl Lemma : bag-mapfilter-null
∀P,f,bs:Top. (null(bag-mapfilter(f;P;bs)) ~ null([x∈bs|P x]))
Proof
Definitions occuring in Statement :
bag-mapfilter: bag-mapfilter(f;P;bs),
bag-filter: [x∈b|p[x]],
null: null(as),
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
bag-mapfilter: bag-mapfilter(f;P;bs),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
bag-map-null,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}P,f,bs:Top. (null(bag-mapfilter(f;P;bs)) \msim{} null([x\mmember{}bs|P x]))
Date html generated:
2016_05_15-PM-02_23_49
Last ObjectModification:
2015_12_27-AM-09_53_51
Theory : bags
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