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Step * 1 1 1 of Lemma derivative-rsqrt


1. d(e^(r1/r(2)) * rlog(x))/dx = λx.e^(r1/r(2)) * rlog(x) * (r1/r(2)) * (r1/x) on (r0, ∞)
2. x : ℝ
3. [%2] : r0 < x
⊢ r0 < (r(2) * rsqrt(x))
BY
{ ((InstLemma `rsqrt-positive` [⌜x⌝]⋅ THENM RWO "rmul-is-positive" 0) THEN Auto) }

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Latex:

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Latex:

1.  d(e\^{}(r1/r(2))  *  rlog(x))/dx  =  \mlambda{}x.e\^{}(r1/r(2))  *  rlog(x)  *  (r1/r(2))  *  (r1/x)  on  (r0,  \minfty{})
2.  x  :  \mBbbR{}
3.  [\%2]  :  r0  <  x
\mvdash{}  r0  <  (r(2)  *  rsqrt(x))


By

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Latex:
((InstLemma  `rsqrt-positive`  [\mkleeneopen{}x\mkleeneclose{}]\mcdot{}  THENM  RWO  "rmul-is-positive"  0)  THEN  Auto)

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