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Proof step 3 from proof coef-fac-divides-h (previous step)

User applied rule cut formula

And obtained the following new goals

Proof step 4:
fac(j) * fac(i - j) | (i - j) * fac(i - 1) + j * fac(i - 1), fac(j) * fac(i - j) | (i - j) * fac(i - 1), fac(j) * fac(i - j) | j * fac(i - 1), fac(j - 1) * fac(i - j) | fac(i - 1), fac(j) * fac(i - 1 + j) | fac(i - 1), 0 < j, j < i, 0 ≤ j, 1 < i, 0 < i ⊦ fac(j) * fac(i - j) | fac(i)

Rule argument

fma: fac(j) * fac(i - j) | (i - j) * fac(i - 1) + j * fac(i - 1)

Additional information

Used simplifier rules: divides-add: ⊦ i | j → (i | j + j0 ↔ i | j0); from specification int-gcd%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs Used formulas: fac(j) * fac(i - j) | (i - j) * fac(i - 1) + j * fac(i - 1)