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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