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Proof step 9 from proof mkDecimal-maxScale-le-scale (previous step)

i % 10 = 0, maxScale(i) ≤ abs(j), ∀ i0, j. i→n(i0) < i→n(i) → maxScale(i0) ≤ abs(j) → abs(j) = mkDecimal(i0, j).scale + maxScale(i0) ⊦ j = 0, i = 0, abs(j) = mkDecimal(i / 10, abs(j) - 1).scale + maxScale(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i % 10 = 0 ∧ i ≠ 0 → maxScale(i) = maxScale(i / 10) + 1
Proof step 11:
i % 10 = 0 ∧ i ≠ 0, i % 10 = 0, maxScale(i / 10) + 1 ≤ abs(j), ∀ i0, j. i→n(i0) < i→n(i) → maxScale(i0) ≤ abs(j) → abs(j) = mkDecimal(i0, j).scale + maxScale(i0) ⊦ j = 0, i = 0, abs(j) = mkDecimal(i / 10, abs(j) - 1).scale + maxScale(i / 10) + 1

Rule argument

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

Additional information

Used terms: i