Nuprl Lemma : bag-combine-cons-left
∀[b,a,f:Top]. (⋃x∈a.b.f[x] ~ f[a] + ⋃x∈b.f[x])
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
bag-append: as + bs,
cons-bag: x.b,
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],
top: Top,
all: ∀x:A. B[x]
Lemmas referenced :
bag-map-cons,
bag_union_cons_lemma,
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,
dependent_functionElimination,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[b,a,f:Top]. (\mcup{}x\mmember{}a.b.f[x] \msim{} f[a] + \mcup{}x\mmember{}b.f[x])
Date html generated:
2016_05_15-PM-02_28_41
Last ObjectModification:
2015_12_27-AM-09_50_00
Theory : bags
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