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Proof step 36 from proof coef-sub-mult (previous step)

0 ≤ i, 0 ≤ j, fac(i + 1 - j) * fac(j - 1) | fac(i), fac(i - j) * j * fac(j - 1) | fac(i), 0 < j, 0 < i, j ≤ i, fac(i - j) | fac(i) * fac(i + 1 - j) ⊦ fac(i) * fac(i + 1 - j) = fac(i) * ((i + 1 - 2 * j) * fac(i - j) + fac(i - j) * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0)
Proof step 38:
fac(i) ≠ 0, 0 ≤ i, 0 ≤ j, fac(i + 1 - j) * fac(j - 1) | fac(i), fac(i - j) * j * fac(j - 1) | fac(i), 0 < j, 0 < i, j ≤ i, fac(i - j) | fac(i) * fac(i + 1 - j) ⊦ fac(i + 1 - j) = (i + 1 - 2 * j) * fac(i - j) + fac(i - j) * j

Rule argument

spec: int-mult inst: name: eq-nonzero seq: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0) subst: [j0, j, i] → [(i + 1 - 2 * j) * fac(i - j) + fac(i - j) * j, fac(i + 1 - j), fac(i)] flags: rewrite

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0; Used terms: (i + 1 - 2 * j) * fac(i - j) + fac(i - j) * j, fac(i + 1 - j), fac(i)