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Step * of Lemma integral-rsub

∀[a,b:ℝ]. ∀[f,g:{f:[rmin(a;b), rmax(a;b)] ⟶ℝ| ifun(f;[rmin(a;b), rmax(a;b)])} ].
  (a_∫-b f[x] - g[x] dx = (a_∫-b f[x] dx - a_∫-b g[x] dx))
BY
{ (Auto
   THEN (Assert a_∫-b f[x] - g[x] dx = a_∫-b f[x] + (r(-1) * g[x]) dx BY
               (BLemma `integral_functionality` THEN Auto THEN nRNorm 0 THEN Auto))
   THEN RWW "-1 integral-radd integral-rmul-const" 0
   THEN Auto) }

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Latex:

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


By

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Latex:
(Auto
  THEN  (Assert  a\_\mint{}\msupminus{}b  f[x]  -  g[x]  dx  =  a\_\mint{}\msupminus{}b  f[x]  +  (r(-1)  *  g[x])  dx  BY
                          (BLemma  `integral\_functionality`  THEN  Auto  THEN  nRNorm  0  THEN  Auto))
  THEN  RWW  "-1  integral-radd  integral-rmul-const"  0
  THEN  Auto)

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