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Step * of Lemma sinh-rless

∀x,y:ℝ.  sinh(x) < sinh(y) supposing x < y
BY
{ (InstLemma `derivative-implies-strictly-increasing`       [⌜(-∞, ∞)⌝;⌜λ2x.sinh(x)⌝;⌜λ2x.cosh(x)⌝]⋅ THEN Auto) }

1
.....antecedent..... 
cosh(x) continuous for x ∈ (-∞, ∞)

2
1. x : {x:ℝ| x ∈ (-∞, ∞)} 
⊢ r0 < cosh(x)

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Latex:

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Latex:
\mforall{}x,y:\mBbbR{}.    sinh(x)  <  sinh(y)  supposing  x  <  y


By

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Latex:
(InstLemma  `derivative-implies-strictly-increasing` 
            [\mkleeneopen{}(-\minfty{},  \minfty{})\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.sinh(x)\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.cosh(x)\mkleeneclose{}]\mcdot{}
  THEN  Auto
  )

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