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Proof step 10 from proof maxScale-pot10-01 (previous step)

0 ≤ j, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 → maxScale(i * 10 ^ j0) = j0 ∨ i % 10 = 0 ⊦ i % 10 = 0, maxScale(i * 10 ^ (j - 1) * 10) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i % 10 = 0 ∧ i ≠ 0 → maxScale(i) = maxScale(i / 10) + 1
Proof step 12:
¬((i * 10 ^ (j - 1) * 10) % 10 = 0 ∧ i * 10 ^ (j - 1) * 10 ≠ 0), 0 ≤ j, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 → maxScale(i * 10 ^ j0) = j0 ∨ i % 10 = 0 ⊦ i % 10 = 0, maxScale(i * 10 ^ (j - 1) * 10) = j
Proof step 15:
(i * 10 ^ (j - 1) * 10) % 10 = 0 ∧ i * 10 ^ (j - 1) * 10 ≠ 0, 0 ≤ j, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 → maxScale(i * 10 ^ j0) = j0 ∨ i % 10 = 0 ⊦ i % 10 = 0, maxScale((i * 10 ^ (j - 1) * 10) / 10) + 1 = j

Rule argument

spec: inst: name: maxScale-rec seq: ⊦ i % 10 = 0 ∧ i ≠ 0 → maxScale(i) = maxScale(i / 10) + 1 subst: [i] → [i * 10 ^ (j - 1) * 10] flags: rewrite, current

Additional information

Used terms: i * 10 ^ (j - 1) * 10