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Step * 1 of Lemma vec-midpoint-dist


1. n : ℕ
2. a : ℝ^n
3. b : ℝ^n
4. |(r1/r(2))| = (r1/r(2))
⊢ a - vec-midpoint(a;b)⋅a - vec-midpoint(a;b) = (r1/r(2))*a - (r1/r(2))*b⋅(r1/r(2))*a - (r1/r(2))*b
BY
{ (Assert ⌜req-vec(n;a - vec-midpoint(a;b);(r1/r(2))*a - (r1/r(2))*b)⌝⋅ THENM (RWO "-1" 0 THEN Auto)) }

1
.....assertion..... 
1. n : ℕ
2. a : ℝ^n
3. b : ℝ^n
4. |(r1/r(2))| = (r1/r(2))
⊢ req-vec(n;a - vec-midpoint(a;b);(r1/r(2))*a - (r1/r(2))*b)

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Latex:

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Latex:

1.  n  :  \mBbbN{}
2.  a  :  \mBbbR{}\^{}n
3.  b  :  \mBbbR{}\^{}n
4.  |(r1/r(2))|  =  (r1/r(2))
\mvdash{}  a  -  vec-midpoint(a;b)\mcdot{}a  -  vec-midpoint(a;b)  =  (r1/r(2))*a  -  (r1/r(2))*b\mcdot{}(r1/r(2))*a  -  (r1/r(2))*b


By

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Latex:
(Assert  \mkleeneopen{}req-vec(n;a  -  vec-midpoint(a;b);(r1/r(2))*a  -  (r1/r(2))*b)\mkleeneclose{}\mcdot{}  THENM  (RWO  "-1"  0  THEN  Auto))

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