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Proof step 74 from proof sub-def-any (previous step)

¬ 0 < abs(j0), mkDecimal(j1, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal((j1 * 10 ^ abs(j0) - i0 * 10 ^ (abs(j) - 1)) * 10, abs(j0) + abs(j)), 0 < abs(j0) + abs(j), ∀ 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, (j1 * 10) * 10 ^ abs(j0) = (j1 * 10 ^ abs(j0) - i0 * 10 ^ (abs(j) - 1)) * 10 + i0 * 10 ^ abs(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
mkDecimal(j1, abs(j) - 1) - mkDecimal(i0, 0) = mkDecimal((j1 - i0 * 10 ^ (abs(j) - 1)) * 10, abs(j)), ∀ 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, 10 * j1 = (j1 - i0 * 10 ^ (abs(j) - 1)) * 10 + i0 * 10 ^ abs(j)

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%add-zero: ⊦ i + 0 = i; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs