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Proof step 16 from proof mkDecimal-enlarge (previous step)

mkDecimal(i, j) = mkDecimal(i * 10 ^ (j0 - 1), abs(j) + (j0 - 1)), 0 ≤ j0, 0 < j0, ∀ j1, i, j. i→n(j1) < i→n(j0) → 0 ≤ j1 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j1, abs(j) + j1) ⊦ abs(j) + j0 = 0, mkDecimal(i, j) = mkDecimal(i * 10 ^ (j0 - 1), abs(abs(j) + j0) - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
mkDecimal(i, j) = mkDecimal(i * 10 ^ (j0 - 1), abs(j) + j0 - 1), 0 ≤ j0, 0 < j0, ∀ j1, i, j. i→n(j1) < i→n(j0) → 0 ≤ j1 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j1, abs(j) + j1) ⊦ abs(j) + j0 = 0, mkDecimal(i, j) = mkDecimal(i * 10 ^ (j0 - 1), abs(abs(j) + j0) - 1)

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs