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Proof step 25 from proof max_exp-fac-rec (previous step)

0 < fac(i - 1), prime(i), j0 < i, 0 ≤ j0, 0 < i, i | fac(i - 1), ∀ j1, i, j0. i→n(j1) < i→n(1) → true → prime(i) ∧ 0 < j1 ∧ 0 ≤ j0 ∧ j0 < i → max_exp(i, fac(i * j1 + j0)) = j1 + max_exp(i, fac(j1)) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: prime-fac-divides-not seq: ⊦ prime(i) ∧ j < i ∧ 0 < j → ¬ i | fac(j) subst: [j, i] → [i - 1, i] flags: rewrite, current

Additional information

Used simplifier rules: fac-zero: ⊦ i ≤ 0 → fac(i) = 1;%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%ler: ⊦ i ≤ i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%sub-eq-01: ⊦ i = j → i - j = 0; from specification int-abs%div-one-pos: ⊦ 0 < i → (i | 1 ↔ i = 1); from specification int-gcd%bet-01: ⊦ 0 ≤ i → (i < 1 ↔ i = 0); from specification int-abs%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd Used terms: i - 1, i