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Step * 2 1 1 of Lemma rcos-1-implies-at-least-2pi


1. x : {x:ℝ| r0 < x} 
2. rcos(x) = r1
3. rcos(x) strictly-decreasing for x ∈ [r0, π]
4. iproper([π, 2 * π])
⊢ d(rcos(x))/dx = λx.-(rsin(x)) on [π, 2 * π]
BY
{ ((InstLemma `derivative_functionality_wrt_subinterval` [⌜(-∞, ∞)⌝]⋅ THENM BHyp -1 )
   THEN Auto
   THEN D 0
   THEN Reduce 0
   THEN Auto) }

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Latex:

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Latex:

1.  x  :  \{x:\mBbbR{}|  r0  <  x\} 
2.  rcos(x)  =  r1
3.  rcos(x)  strictly-decreasing  for  x  \mmember{}  [r0,  \mpi{}]
4.  iproper([\mpi{},  2  *  \mpi{}])
\mvdash{}  d(rcos(x))/dx  =  \mlambda{}x.-(rsin(x))  on  [\mpi{},  2  *  \mpi{}]


By

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Latex:
((InstLemma  `derivative\_functionality\_wrt\_subinterval`  [\mkleeneopen{}(-\minfty{},  \minfty{})\mkleeneclose{}]\mcdot{}  THENM  BHyp  -1  )
  THEN  Auto
  THEN  D  0
  THEN  Reduce  0
  THEN  Auto)

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