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Proof step 8 from proof coef-fac-divides (previous step)

1 < i, 0 < i, ∀ i0, j. i→n(i0) < i→n(i) → j ≤ i0 ∧ 0 < j ∧ 0 < i0 → fac(j) * fac(i0 - j) | fac(i0) ⊦ fac(i - 1) | fac(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < i → fac(i) = i * fac(i - 1)

Rule argument

spec: inst: name: fac-rec seq: ⊦ 0 < i → fac(i) = i * fac(i - 1) subst: [i] → [i] flags: rewrite, current

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i