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Proof step 16 from proof mkDecimal-maxScale-nle-int (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = i / (10 * 10 ^ (abs(j) - 1)), abs(j) ≤ maxScale(i / 10), ∀ i0, j. i→n(i0) < i→n(i) → abs(j) < maxScale(i0) → mkDecimal(i0, j).int = i0 / 10 ^ abs(j) ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ abs(j), i = 0

Rule argument

Additional information

Used simplifier rules: abs-10: ⊦ abs(i) - 1 < 0 ↔ i = 0; from specification int-abs%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot