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Step * 1 of Lemma real-vec-norm-equal-iff


1. n : ℕ
2. x : ℝ^n
3. y : ℝ^n
⊢ uiff((x⋅x = ||y||^2) ∧ (r0 ≤ ||y||);x⋅x = y⋅y)
BY
{ (RWO "real-vec-norm-squared" 0 THEN Auto) }

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Latex:

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Latex:

1.  n  :  \mBbbN{}
2.  x  :  \mBbbR{}\^{}n
3.  y  :  \mBbbR{}\^{}n
\mvdash{}  uiff((x\mcdot{}x  =  ||y||\^{}2)  \mwedge{}  (r0  \mleq{}  ||y||);x\mcdot{}x  =  y\mcdot{}y)


By

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Latex:
(RWO  "real-vec-norm-squared"  0  THEN  Auto)

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