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Proof step 22 from proof mkDecimal-maxScale-le-int (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
mkDecimal(i / 10, abs(j) - 1).int = i / (10 * 10 ^ maxScale(i / 10)), i % 10 = 0, maxScale(i / 10) < abs(j), ∀ i0, j. i→n(i0) < i→n(i) → maxScale(i0) ≤ abs(j) → mkDecimal(i0, j).int = i0 / 10 ^ maxScale(i0) ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ (maxScale(i / 10) + 1), i = 0

Rule argument

Additional information

Used simplifier rules: maxScale-not-negt: ⊦ ¬ maxScale(i) < 0;%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot