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Proof step 68 from proof sub-def-any (previous step)

¬ ¬ abs(j0) + abs(j) - 1 < 0, mkDecimal(j1, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal((j1 * 10 ^ abs(j0) - i0 * 10 ^ (abs(j) - 1)) * 10, abs(abs(j0) + abs(j) - 1) + 1), ∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(j1 * 10) + i→n(i0) → true → mkDecimal(i1, j) - mkDecimal(i2, j0) = mkDecimal(i1 * 10 ^ abs(j0) - i2 * 10 ^ abs(j), abs(j) + abs(j0)) ⊦ j = 0, mkDecimal((j1 * 10 ^ abs(j0) - i0 * 10 ^ (abs(j) - 1)) * 10, abs(abs(j0) + abs(j) - 1) + 1) = mkDecimal((j1 * 10) * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 69:
mkDecimal(j1, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal((j1 * 10 ^ abs(j0) - i0 * 10 ^ (abs(j) - 1)) * 10, 2 - abs(j0) + abs(j)), abs(j0) + abs(j) ≤ 0, ∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(j1 * 10) + i→n(i0) → true → mkDecimal(i1, j) - mkDecimal(i2, j0) = mkDecimal(i1 * 10 ^ abs(j0) - i2 * 10 ^ abs(j), abs(j) + abs(j0)) ⊦ j = 0, mkDecimal((j1 * 10 ^ abs(j0) - i0 * 10 ^ (abs(j) - 1)) * 10, 2 - abs(j0) + abs(j)) = mkDecimal((j1 * 10) * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0))

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; 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%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%minus-02: ⊦ ~(i - 1) = ~ i + 1; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs