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Step * of Lemma sum-in-vs-neg

∀[K:Rng]. ∀[vs:VectorSpace(K)]. ∀[n,m:ℤ]. ∀[f:{n..m + 1-} ⟶ Point(vs)].
  (Σ{-(f[i]) | n≤i≤m} = -(Σ{f[i] | n≤i≤m}) ∈ Point(vs))
BY
{ (Auto THEN Unfold `vs-neg` 0 THEN RWO "sum-in-vs-mul" 0 THEN Auto) }

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Latex:

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Latex:
\mforall{}[K:Rng].  \mforall{}[vs:VectorSpace(K)].  \mforall{}[n,m:\mBbbZ{}].  \mforall{}[f:\{n..m  +  1\msupminus{}\}  {}\mrightarrow{}  Point(vs)].
    (\mSigma{}\{-(f[i])  |  n\mleq{}i\mleq{}m\}  =  -(\mSigma{}\{f[i]  |  n\mleq{}i\mleq{}m\}))


By

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Latex:
(Auto  THEN  Unfold  `vs-neg`  0  THEN  RWO  "sum-in-vs-mul"  0  THEN  Auto)

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