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Proof step 6 from proof max_exp-fac-smaller (previous step)

0 < j, 1 < i, 0 < i, 0 < j, j < i, prime(i), ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ j0 < i ∧ 0 < j0 ∧ 0 < i ∧ 1 < i → max_exp(i, fac(j0)) = 0 ⊦ max_exp(i, j * fac(j - 1)) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 0 < j ∧ 0 < j0 ∧ prime(i) → max_exp(i, j * j0) = max_exp(i, j) + max_exp(i, j0)
Proof step 8:
0 < j ∧ 0 < fac(j - 1) ∧ prime(i), 0 < j, 1 < i, 0 < i, 0 < j, j < i, prime(i), ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ j0 < i ∧ 0 < j0 ∧ 0 < i ∧ 1 < i → max_exp(i, fac(j0)) = 0 ⊦ max_exp(i, j) + max_exp(i, fac(j - 1)) = 0

Rule argument

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

Additional information

Used simplifier rules: fac-pos-01: ⊦ ¬ fac(i) ≤ 0;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: fac(j - 1), j, i