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Proof step 31 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), abs(j) + abs(j0) - 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), abs(j) + abs(j0) - 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

Proof step 32:
⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)
Proof step 33:
0 ≤ 1, mkDecimal(i, j) - mkDecimal(j1, abs(j0) - 1) = mkDecimal((i * 10 ^ (abs(j0) - 1) - j1 * 10 ^ abs(j)) * 10 ^ 1, 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 ^ 1, 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

Rule argument

spec: decimal inst: name: mkDecimal-enlarge seq: ⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0) subst: [j0, j, i] → [1, abs(j) + abs(j0) - 1, i * 10 ^ (abs(j0) - 1) - j1 * 10 ^ abs(j)] flags: rewrite

Additional information

Used terms: 1, abs(j) + abs(j0) - 1, i * 10 ^ (abs(j0) - 1) - j1 * 10 ^ abs(j)