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Proof step 12 from proof coef-fac-divides (previous step)

fac(j) * fac(i - 1 - j) | fac(i - 1), 0 < j, j < i, 1 < i, 0 < i, fac(j - 1) * fac(i - j) | fac(i - 1), ∀ i0, j. i→n(i0) < i→n(i) → j ≤ i0 ∧ 0 < j ∧ 0 < i0 → fac(j) * fac(i0 - j) | fac(i0) ⊦ i = j, fac(j) * fac(i - j) | fac(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
0 < j, j < i, 1 < i, 0 < i, fac(j - 1) * fac(i - j) | fac(i - 1), fac(j) * fac(i - 1 + j) | fac(i - 1), ∀ i0, j. i→n(i0) < i→n(i) → j ≤ i0 ∧ 0 < j ∧ 0 < i0 → fac(j) * fac(i0 - j) | fac(i0) ⊦ i = j, fac(j) * fac(i - j) | fac(i)

Rule argument

Additional information

Used simplifier rules: sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs