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Proof step 34 from proof sub-def-any (previous step)

mkDecimal(i, j) - mkDecimal(j1, abs(j0) - 1) = mkDecimal((i * 10 ^ (abs(j0) - 1) - j1 * 10 ^ abs(j)) * 10, abs(abs(j) + abs(j0) - 1) + 1), ∀ 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, mkDecimal((i * 10 ^ (abs(j0) - 1) - j1 * 10 ^ abs(j)) * 10, abs(abs(j) + abs(j0) - 1) + 1) = mkDecimal(i * 10 ^ abs(j0) - (j1 * 10) * 10 ^ abs(j), abs(j) + abs(j0)), i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [abs(j) + abs(j0) - 1] flags: rewrite

Additional information

Used terms: abs(j) + abs(j0) - 1