Nuprl Lemma : bag-mapfilter-empty
∀P,f:Top. (bag-mapfilter(f;P;{}) ~ {})
Proof
Definitions occuring in Statement :
bag-mapfilter: bag-mapfilter(f;P;bs),
empty-bag: {},
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
empty-bag: {},
bag-mapfilter: bag-mapfilter(f;P;bs),
bag-filter: [x∈b|p[x]],
bag-map: bag-map(f;bs),
member: t ∈ T,
top: Top
Lemmas referenced :
filter_nil_lemma,
map_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis
Latex:
\mforall{}P,f:Top. (bag-mapfilter(f;P;\{\}) \msim{} \{\})
Date html generated:
2016_05_15-PM-02_23_50
Last ObjectModification:
2015_12_27-AM-09_53_50
Theory : bags
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