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Step * 2 of Lemma rcos-nonneg


1. x : {x:ℝ| x ∈ [-(π/2), π/2]} 
2. x < (r1/r(1000))
⊢ r0 ≤ rcos(x)
BY
{ ((InstLemma `rless-cases` [⌜(r(-1)/r(1000))⌝;⌜r0⌝;⌜x⌝]⋅ THENA (Auto THEN nRMul ⌜r(1000)⌝ 0⋅ THEN Auto)) THEN D -1) }

1
1. x : {x:ℝ| x ∈ [-(π/2), π/2]} 
2. x < (r1/r(1000))
3. (r(-1)/r(1000)) < x
⊢ r0 ≤ rcos(x)

2
1. x : {x:ℝ| x ∈ [-(π/2), π/2]} 
2. x < (r1/r(1000))
3. x < r0
⊢ r0 ≤ rcos(x)

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Latex:

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Latex:

1.  x  :  \{x:\mBbbR{}|  x  \mmember{}  [-(\mpi{}/2),  \mpi{}/2]\} 
2.  x  <  (r1/r(1000))
\mvdash{}  r0  \mleq{}  rcos(x)


By

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Latex:
((InstLemma  `rless-cases`  [\mkleeneopen{}(r(-1)/r(1000))\mkleeneclose{};\mkleeneopen{}r0\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}
    THENA  (Auto  THEN  nRMul  \mkleeneopen{}r(1000)\mkleeneclose{}  0\mcdot{}  THEN  Auto)
    )
  THEN  D  -1
  )

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