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Proof step 17 from proof max_exp-fac-rec (previous step)

0 < i, 0 ≤ j0, j0 < i, prime(i), 0 < j, 0 < fac(i * j - 1), 0 < fac(j - 1), ∀ 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) + max_exp(i, fac(i * j - 1)) = j + max_exp(i, j) + max_exp(i, fac(j - 1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ 0 < j ∧ 0 < j0 ∧ prime(i) → max_exp(i, j * j0) = max_exp(i, j) + max_exp(i, j0)
Proof step 19:
0 < i ∧ 0 < j ∧ prime(i), 0 < i, 0 ≤ j0, j0 < i, prime(i), 0 < j, 0 < fac(i * j - 1), 0 < fac(j - 1), ∀ 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) + max_exp(i, j)) + max_exp(i, fac(i * j - 1)) = j + max_exp(i, j) + max_exp(i, fac(j - 1))

Rule argument

spec: inst: name: max_exp-mult seq: ⊦ 0 < j ∧ 0 < j0 ∧ prime(i) → max_exp(i, j * j0) = max_exp(i, j) + max_exp(i, j0) subst: [j0, j, i] → [j, i, i] flags: rewrite, current

Additional information

Used terms: j, i, i