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Proof step 2 from proof coef-fac-divides-h (previous step)

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)

User applied rule cut formula

And obtained the following new goals

Proof step 3:
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)
Proof step 9:
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) | (i - j) * fac(i - 1), fac(j) * fac(i - j) | fac(i)

Rule argument

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

Additional information

Used formulas: fac(j) * fac(i - j) | (i - j) * fac(i - 1)