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Proof step 26 from proof coef-rec-add-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ j | i ∧ i ≠ 0 → i % j = 0

Rule argument

spec: int-gcd inst: name: div-mod-zero seq: ⊦ j | i ∧ i ≠ 0 → i % j = 0 subst: [j, i] → [fac(i - j) * fac(j - 1), fac(i - 1)] flags: rewrite

Additional information

Used simplifier rules: fac-zero-02: ⊦ fac(i) ≠ 0;%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: fac(i - j) * fac(j - 1), fac(i - 1)