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Step * of Lemma rsum-split2

∀[n,m:ℤ]. ∀[k:{n..m + 1-}]. ∀[x:{n..m + 1-} ⟶ ℝ].  (Σ{x[i] | n≤i≤m} = (Σ{x[i] | n≤i≤k} + Σ{x[i] | k + 1≤i≤m}))
BY
{ (InstLemma `rsum-split` [] THEN RepeatFor 2 (ParallelLast') THEN Auto) }

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Latex:

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Latex:
\mforall{}[n,m:\mBbbZ{}].  \mforall{}[k:\{n..m  +  1\msupminus{}\}].  \mforall{}[x:\{n..m  +  1\msupminus{}\}  {}\mrightarrow{}  \mBbbR{}].
    (\mSigma{}\{x[i]  |  n\mleq{}i\mleq{}m\}  =  (\mSigma{}\{x[i]  |  n\mleq{}i\mleq{}k\}  +  \mSigma{}\{x[i]  |  k  +  1\mleq{}i\mleq{}m\}))


By

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Latex:
(InstLemma  `rsum-split`  []  THEN  RepeatFor  2  (ParallelLast')  THEN  Auto)

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