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Proof step 5 from proof max_exp-mult-01 (previous step)

i | j, 0 < j0, 0 < j, prime(i), ∀ i0, j1, j0. i→n(max_exp(i0, j1)) < i→n(max_exp(i, j)) → prime(i0) ∧ 0 < j1 ∧ 0 < j0 → max_exp(i0, j1 * j0) = max_exp(i0, j1) + max_exp(i0, j0) ⊦ max_exp(i, j * j0) = max_exp(i, j) + max_exp(i, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ prime(i) ∧ i | j ∧ 0 < j → max_exp(i, j) = max_exp(i, j / i) + 1
Proof step 7:
prime(i) ∧ i | j ∧ 0 < j, i | j, 0 < j0, 0 < j, prime(i), ∀ i0, j1, j0. i→n(max_exp(i0, j1)) < i→n(max_exp(i, j / i) + 1) → prime(i0) ∧ 0 < j1 ∧ 0 < j0 → max_exp(i0, j1 * j0) = max_exp(i0, j1) + max_exp(i0, j0) ⊦ max_exp(i, j * j0) = (max_exp(i, j / i) + 1) + max_exp(i, j0)

Rule argument

spec: inst: name: max_exp-rec seq: ⊦ prime(i) ∧ i | j ∧ 0 < j → max_exp(i, j) = max_exp(i, j / i) + 1 subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i