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Step * of Lemma rsum-split-first

∀[n,m:ℤ]. ∀[x:{n..m + 1-} ⟶ ℝ].  Σ{x[i] | n≤i≤m} = (x[n] + Σ{x[i] | n + 1≤i≤m}) supposing n ≤ m
BY
{ (Auto THEN InstLemma `rsum-split` [⌜n⌝;⌜m⌝;⌜x⌝;⌜n⌝]⋅ THEN Auto THEN RWO "rsum-single" (-1) THEN Auto) }

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Latex:

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


By

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Latex:
(Auto
  THEN  InstLemma  `rsum-split`  [\mkleeneopen{}n\mkleeneclose{};\mkleeneopen{}m\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  RWO  "rsum-single"  (-1)
  THEN  Auto)

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