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Proof step 3 from proof max_exp-fac-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ prime(i) ∧ 0 < j ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j + j0)) = max_exp(i, fac(i * j))
Proof step 5:
prime(i) ∧ 0 < j ∧ 0 ≤ j0 ∧ j0 < i, prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i, ∀ 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)) ⊦ max_exp(i, fac(i * j)) = j + max_exp(i, fac(j))

Rule argument

spec: inst: name: max_exp-fac-add seq: ⊦ prime(i) ∧ 0 < j ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j + j0)) = max_exp(i, fac(i * j)) subst: [j0, j, i] → [j0, j, i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: j0, j, i