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Step * of Lemma integral-additive

∀[a,b,c:ℝ]. ∀[f:{f:[rmin(a;rmin(b;c)), rmax(a;rmax(b;c))] ⟶ℝ| ifun(f;[rmin(a;rmin(b;c)), rmax(a;rmax(b;c))])} ].
  (a_∫-b f[x] dx = (a_∫-c f[x] dx + c_∫-b f[x] dx))
BY
{ (RepeatFor 3 (Intro) THEN (Assert rmin(a;rmin(b;c)) ≤ rmax(a;rmax(b;c)) BY (BLemma `rmin_lb` THEN Auto)) THEN Intro) }

1
1. [a] : ℝ
2. [b] : ℝ
3. [c] : ℝ
4. rmin(a;rmin(b;c)) ≤ rmax(a;rmax(b;c))
5. [f] : {f:[rmin(a;rmin(b;c)), rmax(a;rmax(b;c))] ⟶ℝ| ifun(f;[rmin(a;rmin(b;c)), rmax(a;rmax(b;c))])} 
⊢ a_∫-b f[x] dx = (a_∫-c f[x] dx + c_∫-b f[x] dx)

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Latex:

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Latex:
\mforall{}[a,b,c:\mBbbR{}].  \mforall{}[f:\{f:[rmin(a;rmin(b;c)),  rmax(a;rmax(b;c))]  {}\mrightarrow{}\mBbbR{}| 
                                  ifun(f;[rmin(a;rmin(b;c)),  rmax(a;rmax(b;c))])\}  ].
    (a\_\mint{}\msupminus{}b  f[x]  dx  =  (a\_\mint{}\msupminus{}c  f[x]  dx  +  c\_\mint{}\msupminus{}b  f[x]  dx))


By

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Latex:
(RepeatFor  3  (Intro)
  THEN  (Assert  rmin(a;rmin(b;c))  \mleq{}  rmax(a;rmax(b;c))  BY
                          (BLemma  `rmin\_lb`  THEN  Auto))
  THEN  Intro)

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