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Proof step 15 from proof max_exp-mult-01 (previous step)

max_exp(i, j / i * j0) = max_exp(i, j / i) + max_exp(i, j0), prime(i), 0 < j, i | j, 0 < 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-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [j, i] flags: rewrite

Additional information

Used simplifier rules: max_exp-zero-02: ⊦ prime(i) ∧ 0 < i0 → (max_exp(i, i0) = 0 ↔ ¬ i | i0);%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%eq: ⊦ i = i + j ↔ j = 0; from specification int-basic2%div-zero-zero: ⊦ 0 | i ↔ i = 0; from specification int-gcd%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div Used terms: j, i