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Proof step 19 from proof less-trans (previous step)

0 ≤ abs(i0) + abs(i2), mkDecimal(i1 * 10 ^ (abs(i0) + abs(i4)), abs(i2) + abs(i0) + abs(i4)) < mkDecimal(i3 * 10 ^ (abs(i0) + abs(i2)), abs(abs(i4)) + abs(i0) + abs(i2)), mkDecimal(i, abs(i0)) < mkDecimal(i1 * 10 ^ (abs(i0) + abs(i4)), abs(i2) + abs(i0) + abs(i4)), 0 ≤ abs(i0) + abs(i4) ⊦ mkDecimal(i, abs(i0)) < mkDecimal(i3 * 10 ^ (abs(i0) + abs(i2)), abs(abs(i4)) + abs(i0) + abs(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;%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%abs-01: ⊦ abs(abs(i)) = abs(i); from specification int-abs