Nuprl Lemma : bag-filter-filter
∀[p,q,bs:Top]. ([x∈[x∈bs|p[x]]|q[x]] ~ [x∈bs|p[x] ∧b q[x]])
Proof
Definitions occuring in Statement :
bag-filter: [x∈b|p[x]],
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
bag-filter: [x∈b|p[x]],
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
filter-filter,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[p,q,bs:Top]. ([x\mmember{}[x\mmember{}bs|p[x]]|q[x]] \msim{} [x\mmember{}bs|p[x] \mwedge{}\msubb{} q[x]])
Date html generated:
2016_05_15-PM-02_23_12
Last ObjectModification:
2015_12_27-AM-09_54_15
Theory : bags
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