Nuprl Lemma : bag-summation-empty
∀[add,zero,f:Top].  (Σ(x∈{}). f[x] ~ zero)
Proof
Definitions occuring in Statement : 
bag-summation: Σ(x∈b). f[x]
, 
empty-bag: {}
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
empty-bag: {}
, 
bag-summation: Σ(x∈b). f[x]
, 
bag-accum: bag-accum(v,x.f[v; x];init;bs)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
top: Top
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
list_accum_nil_lemma, 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
sqequalRule, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
isectElimination, 
hypothesisEquality, 
because_Cache
Latex:
\mforall{}[add,zero,f:Top].    (\mSigma{}(x\mmember{}\{\}).  f[x]  \msim{}  zero)
Date html generated:
2016_05_15-PM-02_30_56
Last ObjectModification:
2015_12_27-AM-09_48_28
Theory : bags
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