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Step * 1 1 of Lemma Minkowski-inequality1


1. n : ℕ
2. x : ℝ^n
3. y : ℝ^n
⊢ ||x + y||^2 = (||x||^2 + ||y||^2 + (r(2) * x⋅y))
BY
{ ((RWW "real-vec-norm-squared dot-product-linearity1.1 dot-product-linearity1.2" 0⋅ THENA Auto)
   THEN (RWW "dot-product-linearity2.1 dot-product-linearity2.2" 0⋅ THENA Auto)
   ) }

1
1. n : ℕ
2. x : ℝ^n
3. y : ℝ^n
⊢ ((x⋅x + x⋅y) + y⋅x + y⋅y) = (x⋅x + y⋅y + (r(2) * x⋅y))

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Latex:

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Latex:

1.  n  :  \mBbbN{}
2.  x  :  \mBbbR{}\^{}n
3.  y  :  \mBbbR{}\^{}n
\mvdash{}  ||x  +  y||\^{}2  =  (||x||\^{}2  +  ||y||\^{}2  +  (r(2)  *  x\mcdot{}y))


By

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Latex:
((RWW  "real-vec-norm-squared  dot-product-linearity1.1  dot-product-linearity1.2"  0\mcdot{}  THENA  Auto)
  THEN  (RWW  "dot-product-linearity2.1  dot-product-linearity2.2"  0\mcdot{}  THENA  Auto)
  )

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