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Step * 2 of Lemma r2-perp_wf


1. x : ℝ^2
2. r0 < ||x||
3. r2-perp(x) ∈ ℝ^2
4. x⋅r2-perp(x) = r0
⊢ ||r2-perp(x)|| = r1
BY
{ (RepUR ``real-vec-norm`` 0 THEN Assert ⌜r2-perp(x)⋅r2-perp(x) = r1⌝⋅) }

1
.....assertion..... 
1. x : ℝ^2
2. r0 < ||x||
3. r2-perp(x) ∈ ℝ^2
4. x⋅r2-perp(x) = r0
⊢ r2-perp(x)⋅r2-perp(x) = r1

2
1. x : ℝ^2
2. r0 < ||x||
3. r2-perp(x) ∈ ℝ^2
4. x⋅r2-perp(x) = r0
5. r2-perp(x)⋅r2-perp(x) = r1
⊢ rsqrt(r2-perp(x)⋅r2-perp(x)) = r1

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Latex:

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Latex:

1.  x  :  \mBbbR{}\^{}2
2.  r0  <  ||x||
3.  r2-perp(x)  \mmember{}  \mBbbR{}\^{}2
4.  x\mcdot{}r2-perp(x)  =  r0
\mvdash{}  ||r2-perp(x)||  =  r1


By

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Latex:
(RepUR  ``real-vec-norm``  0  THEN  Assert  \mkleeneopen{}r2-perp(x)\mcdot{}r2-perp(x)  =  r1\mkleeneclose{}\mcdot{})

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