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Proof step 13 from proof max_exp-mult-01 (previous step)

prime(i), 0 < j, i | j, 0 < j0, j / i ≤ 0, j / i < j, j / i < j0, ∀ 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) / i) = max_exp(i, j / i) + max_exp(i, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-lezero seq: ⊦ 0 < j → (i / j ≤ 0 ↔ i < j) subst: [j, i] → [i, j] flags: rewrite

Additional information

Used simplifier rules: div-zero-06: ⊦ i < j ∧ 0 < j ∧ 0 < i → i / j = 0; from specification int-div%div-not-ls: ⊦ i < j ∧ 0 < i → ¬ j | i; from specification int-gcd%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: i, j