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Step * of Lemma integral-int-rdiv

∀[a,b:ℝ]. ∀[f:{f:[rmin(a;b), rmax(a;b)] ⟶ℝ| ifun(f;[rmin(a;b), rmax(a;b)])} ]. ∀[c:ℤ-o].
  (a_∫-b (f[x])/c dx = (a_∫-b f[x] dx)/c)
BY
{ (Auto THEN (InstLemma `integral-rmul-const` [⌜a⌝;⌜b⌝;⌜f⌝;⌜rinv(r(c))⌝]⋅ THENA Auto)) }

1
1. a : ℝ
2. b : ℝ
3. f : {f:[rmin(a;b), rmax(a;b)] ⟶ℝ| ifun(f;[rmin(a;b), rmax(a;b)])} 
4. c : ℤ-o
5. a_∫-b rinv(r(c)) * f[x] dx = (rinv(r(c)) * a_∫-b f[x] dx)
⊢ a_∫-b (f[x])/c dx = (a_∫-b f[x] dx)/c

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Latex:

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


By

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Latex:
(Auto  THEN  (InstLemma  `integral-rmul-const`  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}rinv(r(c))\mkleeneclose{}]\mcdot{}  THENA  Auto))

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