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Step * 1 of Lemma rcos-pi-over-4


1. r0 < rsqrt(r(2))
2. ((r1/rsqrt(r(2)))^2 + rcos((π/r(4)))^2) = r1
⊢ rcos((π/r(4))) = (r1/rsqrt(r(2)))
BY
{ ((Assert r0 < rcos((π/r(4))) BY
          (UseWitness ⌜10⌝⋅ THEN MemTypeCD THEN Auto THEN ByComputation 10000 THEN Auto))
   THEN InstLemma `rsqrt-unique` [⌜(r1/r(2))⌝;⌜rcos((π/r(4)))⌝]⋅
   THEN Auto) }

1
.....antecedent..... 
1. r0 < rsqrt(r(2))
2. ((r1/rsqrt(r(2)))^2 + rcos((π/r(4)))^2) = r1
3. r0 < rcos((π/r(4)))
⊢ (rcos((π/r(4))) * rcos((π/r(4)))) = (r1/r(2))

2
1. r0 < rsqrt(r(2))
2. ((r1/rsqrt(r(2)))^2 + rcos((π/r(4)))^2) = r1
3. r0 < rcos((π/r(4)))
4. rcos((π/r(4))) = rsqrt((r1/r(2)))
⊢ rcos((π/r(4))) = (r1/rsqrt(r(2)))

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Latex:

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Latex:

1.  r0  <  rsqrt(r(2))
2.  ((r1/rsqrt(r(2)))\^{}2  +  rcos((\mpi{}/r(4)))\^{}2)  =  r1
\mvdash{}  rcos((\mpi{}/r(4)))  =  (r1/rsqrt(r(2)))


By

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Latex:
((Assert  r0  <  rcos((\mpi{}/r(4)))  BY
                (UseWitness  \mkleeneopen{}10\mkleeneclose{}\mcdot{}  THEN  MemTypeCD  THEN  Auto  THEN  ByComputation  10000  THEN  Auto))
  THEN  InstLemma  `rsqrt-unique`  [\mkleeneopen{}(r1/r(2))\mkleeneclose{};\mkleeneopen{}rcos((\mpi{}/r(4)))\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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