Nuprl Lemma : bag-combine-assoc
∀[f,g:Top]. ∀[bs:bag(Top)]. (⋃y∈⋃x∈bs.f[x].g[y] ~ ⋃x∈bs.⋃y∈f[x].g[y])
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
bag: bag(T),
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-combine: ⋃x∈bs.f[x],
bag-map: bag-map(f;bs),
bag-union: bag-union(bbs),
top: Top,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
concat-map-assoc,
bag-subtype-list,
bag_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
applyEquality,
dependent_functionElimination,
because_Cache,
hypothesis,
sqequalAxiom
Latex:
\mforall{}[f,g:Top]. \mforall{}[bs:bag(Top)]. (\mcup{}y\mmember{}\mcup{}x\mmember{}bs.f[x].g[y] \msim{} \mcup{}x\mmember{}bs.\mcup{}y\mmember{}f[x].g[y])
Date html generated:
2016_05_15-PM-02_28_09
Last ObjectModification:
2015_12_27-AM-09_50_58
Theory : bags
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