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Step * 2 1 2 of Lemma rcos-positive


1. x : {x:ℝ| x ∈ (-(π/2), π/2)} 
2. x < (r1/r(1000))
3. (r(-1)/r(1000)) < x
4. |x - r0| < (r1/r(1000))
⊢ r0 < rcos(x)
BY
{ (Assert |rcos(x) - rcos(r0)| ≤ |x - r0| BY
         Auto) }

1
1. x : {x:ℝ| x ∈ (-(π/2), π/2)} 
2. x < (r1/r(1000))
3. (r(-1)/r(1000)) < x
4. |x - r0| < (r1/r(1000))
5. |rcos(x) - rcos(r0)| ≤ |x - r0|
⊢ r0 < rcos(x)

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Latex:

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Latex:

1.  x  :  \{x:\mBbbR{}|  x  \mmember{}  (-(\mpi{}/2),  \mpi{}/2)\} 
2.  x  <  (r1/r(1000))
3.  (r(-1)/r(1000))  <  x
4.  |x  -  r0|  <  (r1/r(1000))
\mvdash{}  r0  <  rcos(x)


By

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Latex:
(Assert  |rcos(x)  -  rcos(r0)|  \mleq{}  |x  -  r0|  BY
              Auto)

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