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Proof step 42 from proof sub-def-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: eq-nonzero: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0); from specification int-mult%neq-not-zero: ⊦ i * j ≠ i * j0 → i ≠ 0; (forward) from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult