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Step * of Lemma arctangent-rinv

∀[x:{x:ℝ| x ∈ (r0, ∞)} ]. (arctangent(rinv(x)) = (π/2 - arctangent(x)))
BY
{ (Auto
   THEN nRAdd ⌜arctangent(x)⌝ 0⋅
   THEN InstLemma `antiderivatives-equal` 
   [⌜(r0, ∞)⌝;⌜λ2x.r0⌝;⌜λ2x.arctangent((r1/x)) + arctangent(x)⌝;⌜λ2x.π/2⌝]⋅
   THEN Auto) }

1
.....antecedent..... 
1. x : {x:ℝ| x ∈ (r0, ∞)} 
⊢ d(arctangent((r1/x)) + arctangent(x))/dx = λx.r0 on (r0, ∞)

2
.....antecedent..... 
1. x : {x:ℝ| x ∈ (r0, ∞)} 
⊢ ∃x:{x:ℝ| x ∈ (r0, ∞)} . ((arctangent((r1/x)) + arctangent(x)) = π/2)

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Latex:

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Latex:
\mforall{}[x:\{x:\mBbbR{}|  x  \mmember{}  (r0,  \minfty{})\}  ].  (arctangent(rinv(x))  =  (\mpi{}/2  -  arctangent(x)))


By

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Latex:
(Auto
  THEN  nRAdd  \mkleeneopen{}arctangent(x)\mkleeneclose{}  0\mcdot{}
  THEN  InstLemma  `antiderivatives-equal` 
  [\mkleeneopen{}(r0,  \minfty{})\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.r0\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.arctangent((r1/x))  +  arctangent(x)\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.\mpi{}/2\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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