Step * of Lemma rsum_functionality_wrt_rleq2

[n,m:ℤ]. ∀[x,y:{n..m 1-} ⟶ ℝ].
  Σ{x[k] n≤k≤m} ≤ Σ{y[k] n≤k≤m} supposing ∀k:ℤ((n ≤ k)  (k ≤ m)  (x[k] ≤ y[k]))
BY
(Fold `pointwise-rleq` THEN InstLemma `rsum_functionality_wrt_rleq` [] THEN Trivial) }


Latex:


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


By


Latex:
(Fold  `pointwise-rleq`  0  THEN  InstLemma  `rsum\_functionality\_wrt\_rleq`  []  THEN  Trivial)




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