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Step * of Lemma rabs-difference-cosine-rleq

∀x,y:ℝ.  (|cosine(x) - cosine(y)| ≤ |x - y|)
BY
{ ((InstLemma `mean-value-for-bounded-derivative` [⌜(-∞, ∞)⌝;⌜λ2x.cosine(x)⌝;⌜λ2x.-(sine(x))⌝;⌜r1⌝]⋅ THENA Auto)
   THEN Try ((RWO "-1" 0 THEN Auto))
   THEN Try ((nRNorm 0 THEN Auto))) }

1
1. x : {x:ℝ| x ∈ (-∞, ∞)} 
⊢ |-(sine(x))| ≤ r1

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Latex:

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Latex:
\mforall{}x,y:\mBbbR{}.    (|cosine(x)  -  cosine(y)|  \mleq{}  |x  -  y|)


By

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Latex:
((InstLemma  `mean-value-for-bounded-derivative`  [\mkleeneopen{}(-\minfty{},  \minfty{})\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.cosine(x)\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.-(sine(x))\mkleeneclose{};\mkleeneopen{}r1\mkleeneclose{}]\mcdot{}
    THENA  Auto
    )
  THEN  Try  ((RWO  "-1"  0  THEN  Auto))
  THEN  Try  ((nRNorm  0  THEN  Auto)))

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