Nuprl Lemma : bag-filter-append
∀[p,as,bs:Top].  ([x∈as + bs|p[x]] ~ [x∈as|p[x]] + [x∈bs|p[x]])
Proof
Definitions occuring in Statement : 
bag-filter: [x∈b|p[x]]
, 
bag-append: as + bs
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bag-filter: [x∈b|p[x]]
, 
bag-append: as + bs
, 
top: Top
Lemmas referenced : 
filter_append_sq, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesisEquality, 
hypothesis, 
sqequalAxiom, 
sqequalRule, 
because_Cache
Latex:
\mforall{}[p,as,bs:Top].    ([x\mmember{}as  +  bs|p[x]]  \msim{}  [x\mmember{}as|p[x]]  +  [x\mmember{}bs|p[x]])
Date html generated:
2016_05_15-PM-02_23_09
Last ObjectModification:
2015_12_27-AM-09_54_23
Theory : bags
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