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Step * 1 of Lemma rabs-cosine-rleq


1. x : ℝ
2. (sine(x)^2 + cosine(x)^2) = r1
⊢ |cosine(x)| ≤ r1
BY
{ ((InstLemma `rnexp-rleq-iff` [⌜|cosine(x)|⌝;⌜r1⌝;⌜2⌝]⋅ THENA Auto) THEN (RWO "-1" 0 THENA Auto) THEN Thin (-1)) }

1
1. x : ℝ
2. (sine(x)^2 + cosine(x)^2) = r1
⊢ |cosine(x)|^2 ≤ r1^2

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Latex:

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Latex:

1.  x  :  \mBbbR{}
2.  (sine(x)\^{}2  +  cosine(x)\^{}2)  =  r1
\mvdash{}  |cosine(x)|  \mleq{}  r1


By

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Latex:
((InstLemma  `rnexp-rleq-iff`  [\mkleeneopen{}|cosine(x)|\mkleeneclose{};\mkleeneopen{}r1\mkleeneclose{};\mkleeneopen{}2\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (RWO  "-1"  0  THENA  Auto)
  THEN  Thin  (-1))

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