---

Step * 1 of Lemma component-rleq-real-vec-norm


1. n : ℕ
2. i : ℕn
3. x : ℝ^n
⊢ ((x i) * (x i)) ≤ x⋅x
BY
{ (RepUR ``dot-product`` 0 THEN InstLemma `item-rleq-rsum-of-nonneg` [⌜0⌝;⌜n - 1⌝;⌜λ2i.(x i) * (x i)⌝]⋅ THEN Auto) }

---

Latex:

---

Latex:

1.  n  :  \mBbbN{}
2.  i  :  \mBbbN{}n
3.  x  :  \mBbbR{}\^{}n
\mvdash{}  ((x  i)  *  (x  i))  \mleq{}  x\mcdot{}x


By

---

Latex:
(RepUR  ``dot-product``  0
  THEN  InstLemma  `item-rleq-rsum-of-nonneg`  [\mkleeneopen{}0\mkleeneclose{};\mkleeneopen{}n  -  1\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}i.(x  i)  *  (x  i)\mkleeneclose{}]\mcdot{}
  THEN  Auto)

---

Home Index