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Proof step 11 from proof mkDecimal-maxScale-le-int (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i % 10 = 0 ∧ i ≠ 0 → maxScale(i) = maxScale(i / 10) + 1
Proof step 13:
i % 10 = 0 ∧ i ≠ 0, i % 10 = 0, maxScale(i / 10) + 1 ≤ abs(j), abs(abs(j) - 1) < maxScale(i / 10), ∀ i0, j. i→n(i0) < i→n(i) → maxScale(i0) ≤ abs(j) → mkDecimal(i0, j).int = i0 / 10 ^ maxScale(i0) ⊦ j = 0, i = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ (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