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Proof step 8 from proof max_exp-not-div (previous step)

prime(i), 0 < j0, 0 < j, i | j0, ∀ i0, j1, j. i→n(max_exp(i0, j1)) < i→n(max_exp(i, j0 / i) + 1) → prime(i0) ∧ 0 < j1 ∧ 0 < j → max_exp(i0, j * j1) = max_exp(i0, j1) ∨ i0 | j ⊦ max_exp(i, j * j0) = max_exp(i, j0 / i) + 1, i | j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ prime(i) ∧ i | j ∧ 0 < j → max_exp(i, j) = max_exp(i, j / i) + 1
Proof step 10:
prime(i) ∧ i | j * j0 ∧ 0 < j * j0, prime(i), 0 < j0, 0 < j, i | j0, ∀ i0, j1, j. i→n(max_exp(i0, j1)) < i→n(max_exp(i, j0 / i) + 1) → prime(i0) ∧ 0 < j1 ∧ 0 < j → max_exp(i0, j * j1) = max_exp(i0, j1) ∨ i0 | j ⊦ max_exp(i, (j * j0) / i) + 1 = max_exp(i, j0 / i) + 1, i | j

Rule argument

spec: inst: name: max_exp-rec seq: ⊦ prime(i) ∧ i | j ∧ 0 < j → max_exp(i, j) = max_exp(i, j / i) + 1 subst: [j, i] → [j * j0, i] flags: rewrite, current

Additional information

Used simplifier rules: divides-mult-01: ⊦ i | j → i | j * j0; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult Used terms: j * j0, i