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Step * of Lemma atan_wf

∀[a:{2...}]. ∀[x:ℝ].  atan(a;x) ∈ {y:ℝ| arctangent(x) = y}  supposing |x| ≤ (r1/r(a))
BY
{ (Auto
   THEN (InstLemma `atan_approx-property` [⌜a⌝;⌜x⌝]⋅ THENA Auto)
   THEN (InstLemma `rational-approx-implies-req` [⌜2⌝;⌜arctangent(x)⌝;⌜λN.atan_approx(a;x;N)⌝]⋅
         THENA (Auto THEN Reduce 0 THEN BackThruSomeHyp THEN Auto)
         )
   THEN ProveWfLemma) }

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Latex:

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Latex:
\mforall{}[a:\{2...\}].  \mforall{}[x:\mBbbR{}].    atan(a;x)  \mmember{}  \{y:\mBbbR{}|  arctangent(x)  =  y\}    supposing  |x|  \mleq{}  (r1/r(a))


By

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Latex:
(Auto
  THEN  (InstLemma  `atan\_approx-property`  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (InstLemma  `rational-approx-implies-req`  [\mkleeneopen{}2\mkleeneclose{};\mkleeneopen{}arctangent(x)\mkleeneclose{};\mkleeneopen{}\mlambda{}N.atan\_approx(a;x;N)\mkleeneclose{}]\mcdot{}
              THENA  (Auto  THEN  Reduce  0  THEN  BackThruSomeHyp  THEN  Auto)
              )
  THEN  ProveWfLemma)

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