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Proof step 10 from proof max_exp-mult-01 (previous step)

prime(i) ∧ i | j * j0 ∧ 0 < j * j0, prime(i), 0 < j, 0 < j0, i | j, ∀ 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) + 1 = (max_exp(i, j / i) + 1) + max_exp(i, j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%divides-mult-01: ⊦ i | j → i | j * j0; from specification int-gcd%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2