Step
*
of Lemma
Cauchy-Schwarz-not-strict
∀[n:ℕ]. ∀[x,y:ℝ^n]. (¬(|x⋅y| < (||x|| * ||y||))
⇐⇒ ∀i,j:ℕn. (((x j) * (y i)) = ((x i) * (y j))))
BY
{ ((UnivCD THENA Auto) THEN RWO "Cauchy-Schwarz-strict<" 0 THEN Auto) }
1
1. n : ℕ
2. x : ℝ^n
3. y : ℝ^n
4. ¬(∃i,j:ℕn. (x j) * (y i) ≠ (x i) * (y j))
5. i : ℕn
6. j : ℕn
⊢ ((x j) * (y i)) = ((x i) * (y j))
2
1. n : ℕ
2. x : ℝ^n
3. y : ℝ^n
4. ∀i,j:ℕn. (((x j) * (y i)) = ((x i) * (y j)))
⊢ ¬(∃i,j:ℕn. (x j) * (y i) ≠ (x i) * (y j))
Latex:
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x,y:\mBbbR{}\^{}n]. (\mneg{}(|x\mcdot{}y| < (||x|| * ||y||)) \mLeftarrow{}{}\mRightarrow{} \mforall{}i,j:\mBbbN{}n. (((x j) * (y i)) = ((x i) * (y j))))
By
Latex:
((UnivCD THENA Auto) THEN RWO "Cauchy-Schwarz-strict<" 0 THEN Auto)
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