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Proof step 9 from proof ls-add-01 (previous step)

0 ≤ abs(i2) ⊦ mkDecimal(i * 10 ^ abs(i2), abs(abs(j)) + abs(i2)) < mkDecimal(i1 * 10 ^ abs(j) + i0 * 10 ^ abs(i2), abs(i2) + abs(j)) ↔ mkDecimal(i - i0, j) < mkDecimal(i1, i2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: less-same: ⊦ mkDecimal(i, j) < mkDecimal(i0, j) ↔ i < i0;%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%abs-01: ⊦ abs(abs(i)) = abs(i); from specification int-abs