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Step * of Lemma Riemann-integral-nonneg

∀[a:ℝ]. ∀[b:{b:ℝ| a ≤ b} ]. ∀[f:{f:[a, b] ⟶ℝ| ifun(f;[a, b])} ].
  r0 ≤ ∫ f[x] dx on [a, b] supposing ∀x:ℝ. ((x ∈ [a, b]) ⇒ (r0 ≤ f[x]))
BY
{ ((InstLemma `Riemann-integral-lower-bound` [] THEN RepeatFor 3 (ParallelLast'))
   THEN (D -1 With ⌜r0⌝  THENA Auto)
   THEN ParallelLast
   THEN RWO  "-1<" 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[a:\mBbbR{}].  \mforall{}[b:\{b:\mBbbR{}|  a  \mleq{}  b\}  ].  \mforall{}[f:\{f:[a,  b]  {}\mrightarrow{}\mBbbR{}|  ifun(f;[a,  b])\}  ].
    r0  \mleq{}  \mint{}  f[x]  dx  on  [a,  b]  supposing  \mforall{}x:\mBbbR{}.  ((x  \mmember{}  [a,  b])  {}\mRightarrow{}  (r0  \mleq{}  f[x]))


By

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Latex:
((InstLemma  `Riemann-integral-lower-bound`  []  THEN  RepeatFor  3  (ParallelLast'))
  THEN  (D  -1  With  \mkleeneopen{}r0\mkleeneclose{}    THENA  Auto)
  THEN  ParallelLast
  THEN  RWO    "-1<"  0
  THEN  Auto)

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