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Proof step 4 from proof coef-fac-divides-h (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 6:
fac(j) * fac(i - j) | ((i - j) + 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

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [i0, j, i] → [j, fac(i - 1), i - j] flags: rewrite

Additional information

Used terms: j, fac(i - 1), i - j