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Step * of Lemma rcos-strictly-decreasing

rcos(x) strictly-decreasing for x ∈ [r0, π]
BY
{ ((Assert iproper([r0, π]) BY
          (RepUR ``iproper left-endpoint right-endpoint endpoints`` 0 THEN Auto))
   THEN Using [`f\'',⌜λ2x.-(rsin(x))⌝]
   
      (BLemma `derivative-implies-strictly-decreasing-closed`)⋅
   THEN Auto) }

1
1. iproper([r0, π])
⊢ d(rcos(x))/dx = λx.-(rsin(x)) on [r0, π]

2
1. iproper([r0, π])
⊢ ifun(λx.-(rsin(x));[r0, π])

3
1. iproper([r0, π])
2. x : {x:ℝ| x ∈ [r0, π]} 
⊢ -(rsin(x)) ≤ r0

4
1. iproper([r0, π])
2. x : {x:ℝ| x ∈ (r0, π)} 
⊢ -(rsin(x)) < r0

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Latex:

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Latex:
rcos(x)  strictly-decreasing  for  x  \mmember{}  [r0,  \mpi{}]


By

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Latex:
((Assert  iproper([r0,  \mpi{}])  BY
                (RepUR  ``iproper  left-endpoint  right-endpoint  endpoints``  0  THEN  Auto))
  THEN  Using  [`f\mbackslash{}'',\mkleeneopen{}\mlambda{}\msubtwo{}x.-(rsin(x))\mkleeneclose{}]
 
        (BLemma  `derivative-implies-strictly-decreasing-closed`)\mcdot{}
  THEN  Auto)

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