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Proof step 4 from proof max_exp-div (previous step)

prime(i), ∃ i0. j0 * i0 = j, 0 < j, 0 < j0 ⊦ max_exp(i, j) = max_exp(i, j / j0) + max_exp(i, j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 < j0, prime(i), 0 < i0 ⊦ max_exp(i, j0 * i0) = max_exp(i, i0) + max_exp(i, j0)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult