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Proof step 1 from proof max_exp-fac-rec (conclusion)

⊦ prime(i) ∧ 0 < j ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j + j0)) = j + max_exp(i, fac(j))

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ j1, i, j0. i→n(j1) < i→n(j) → true → prime(i) ∧ 0 < j1 ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j1 + j0)) = j1 + max_exp(i, fac(j1)) ⊦ prime(i) ∧ 0 < j ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j + j0)) = j + max_exp(i, fac(j))

Rule argument

indvar: i→n(j) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j)