Nuprl Lemma : bag-summation-single-sq
∀[add,zero,f,a:Top]. (Σ(x∈{a}). f[x] ~ add f[a] zero)
Proof
Definitions occuring in Statement :
bag-summation: Σ(x∈b). f[x],
single-bag: {x},
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
single-bag: {x},
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_cons_lemma,
istype-void,
list_accum_nil_lemma,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
isect_memberFormation_alt,
axiomSqEquality,
inhabitedIsType,
hypothesisEquality,
isectElimination,
isectIsTypeImplies
Latex:
\mforall{}[add,zero,f,a:Top]. (\mSigma{}(x\mmember{}\{a\}). f[x] \msim{} add f[a] zero)
Date html generated:
2019_10_15-AM-11_00_38
Last ObjectModification:
2019_08_13-PM-00_00_52
Theory : bags
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