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Proof step 9 from proof max_exp-fac-rec (previous step)

0 < i, 0 ≤ j0, j0 < i, prime(i), 0 < j, ∀ j1, i, j0. i→n(j1) < i→n(j) → true → prime(i) ∧ 0 < j1 ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j1 + j0)) = j1 + max_exp(i, fac(j1)) ⊦ max_exp(i, (i * j) * fac(i * j - 1)) = j + max_exp(i, fac(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 0 < i → fac(i) = i * fac(i - 1)
Proof step 11:
0 < j, 0 < i, 0 ≤ j0, j0 < i, prime(i), 0 < j, ∀ j1, i, j0. i→n(j1) < i→n(j) → true → prime(i) ∧ 0 < j1 ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j1 + j0)) = j1 + max_exp(i, fac(j1)) ⊦ max_exp(i, (i * j) * fac(i * j - 1)) = j + max_exp(i, j * fac(j - 1))

Rule argument

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

Additional information

Used terms: j