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Step * 2 of Lemma derivative-rtan

.....antecedent..... 
1. ∀x:{x:ℝ| x ∈ (-(π/2), π/2)} . (r0 < rcos(x))
⊢ d(rcos(x))/dx = λx.-(rsin(x)) on (-(π/2), π/2)
BY
{ (Assert ⌜d(rcos(x))/dx = λx.-(rsin(x)) on (-∞, ∞)⌝⋅ THENA Auto) }

1
1. ∀x:{x:ℝ| x ∈ (-(π/2), π/2)} . (r0 < rcos(x))
2. d(rcos(x))/dx = λx.-(rsin(x)) on (-∞, ∞)
⊢ d(rcos(x))/dx = λx.-(rsin(x)) on (-(π/2), π/2)

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Latex:

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Latex:
.....antecedent..... 
1.  \mforall{}x:\{x:\mBbbR{}|  x  \mmember{}  (-(\mpi{}/2),  \mpi{}/2)\}  .  (r0  <  rcos(x))
\mvdash{}  d(rcos(x))/dx  =  \mlambda{}x.-(rsin(x))  on  (-(\mpi{}/2),  \mpi{}/2)


By

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Latex:
(Assert  \mkleeneopen{}d(rcos(x))/dx  =  \mlambda{}x.-(rsin(x))  on  (-\minfty{},  \minfty{})\mkleeneclose{}\mcdot{}  THENA  Auto)

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