---

Step * of Lemma sum-in-vs-mul

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

---

Latex:

---

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


By

---

Latex:
(Unfold  `sum-in-vs`  0
  THEN  Auto
  THEN  (Assert  [n,  m  +  1)  \mmember{}  bag(\{n..m  +  1\msupminus{}\})  BY
                          Auto)
  THEN  RWO  "vs-bag-add-mul"  0
  THEN  Auto)

---

Home Index