---

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` 0 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)

---

Home Index