Nuprl Lemma : bag-filter-map
∀[f,p,as:Top]. ([x∈bag-map(f;as)|p[x]] ~ bag-map(f;[x∈as|p[f x]]))
Proof
Definitions occuring in Statement :
bag-filter: [x∈b|p[x]],
bag-map: bag-map(f;bs),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-filter: [x∈b|p[x]],
bag-map: bag-map(f;bs),
top: Top,
compose: f o g
Lemmas referenced :
filter-map,
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{}[f,p,as:Top]. ([x\mmember{}bag-map(f;as)|p[x]] \msim{} bag-map(f;[x\mmember{}as|p[f x]]))
Date html generated:
2016_05_15-PM-02_23_20
Last ObjectModification:
2015_12_27-AM-09_54_17
Theory : bags
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