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Step * of Lemma sinh-rleq

∀[x,y:ℝ].  sinh(x) ≤ sinh(y) supposing x ≤ y
BY
{ (InstLemma `derivative-implies-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)  \mleq{}  sinh(y)  supposing  x  \mleq{}  y


By

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Latex:
(InstLemma  `derivative-implies-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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