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Step * 1 of Lemma r2-perp_wf


1. x : ℝ^2
2. r0 < ||x||
3. r2-perp(x) ∈ ℝ^2
⊢ x⋅r2-perp(x) = r0
BY
{ (RepUR ``r2-perp dot-product`` 0
   THEN (RWO "rsum-split-first" 0 THENA Auto)
   THEN Reduce 0
   THEN (RWO "rsum-single" 0 THENA Auto)
   THEN Reduce 0⋅
   THEN nRMul ⌜||x||⌝ 0⋅
   THEN Auto) }

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Latex:

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Latex:

1.  x  :  \mBbbR{}\^{}2
2.  r0  <  ||x||
3.  r2-perp(x)  \mmember{}  \mBbbR{}\^{}2
\mvdash{}  x\mcdot{}r2-perp(x)  =  r0


By

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Latex:
(RepUR  ``r2-perp  dot-product``  0
  THEN  (RWO  "rsum-split-first"  0  THENA  Auto)
  THEN  Reduce  0
  THEN  (RWO  "rsum-single"  0  THENA  Auto)
  THEN  Reduce  0\mcdot{}
  THEN  nRMul  \mkleeneopen{}||x||\mkleeneclose{}  0\mcdot{}
  THEN  Auto)

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