Nuprl Lemma : sum_map_nil_lemma
∀f:Top. (Σf[x] for x ∈ [] ~ 0)
Proof
Definitions occuring in Statement :
sum-map: Σf[x] for x ∈ L,
nil: [],
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
sum-map: Σf[x] for x ∈ L,
select: L[n],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
sum: Σ(f[x] | x < k),
sum_aux: sum_aux(k;v;i;x.f[x])
Lemmas referenced :
base_wf,
stuck-spread,
length_of_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}f:Top. (\mSigma{}f[x] for x \mmember{} [] \msim{} 0)
Date html generated:
2016_05_15-PM-06_25_11
Last ObjectModification:
2016_01_16-PM-00_56_10
Theory : general
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