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Proof step 23 from proof mkDecimal-reduce-int (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = i / (10 * 10 ^ min(maxScale(i / 10), abs(j) - 1)), 0 ≤ min(maxScale(i / 10), abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(i) → true → mkDecimal(i0, j).int = i0 / 10 ^ min(maxScale(i0), abs(j)) ⊦ i = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ min(maxScale(i / 10) + 1, abs(j)), j = 0

Rule argument

Additional information

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