Nuprl Lemma : bag-summation-map
∀[add,zero:Top]. ∀[b:Top List]. ∀[f,g:Top]. (Σ(x∈bag-map(g;b)). f[x] ~ Σ(x∈b). f[g x])
Proof
Definitions occuring in Statement :
bag-summation: Σ(x∈b). f[x],
bag-map: bag-map(f;bs),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
bag-summation: Σ(x∈b). f[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
bag-accum-map,
top_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[add,zero:Top]. \mforall{}[b:Top List]. \mforall{}[f,g:Top]. (\mSigma{}(x\mmember{}bag-map(g;b)). f[x] \msim{} \mSigma{}(x\mmember{}b). f[g x])
Date html generated:
2016_05_15-PM-02_32_24
Last ObjectModification:
2015_12_27-AM-09_47_39
Theory : bags
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