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Proof step 85 from proof equality-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
i % 10 = 0, mkDecimal(i / 10, abs(j) - 1) = mkDecimal(i0, j0) ↔ i / 10 * 10 ^ abs(j0) = i0 * 10 ^ (abs(j) - 1), ∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → true → (mkDecimal(i1, j) = mkDecimal(i2, j0) ↔ i1 * 10 ^ abs(j0) = i2 * 10 ^ abs(j)) ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1) = mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) = i0 * 10 ^ abs(j)

Rule argument

Additional information

Used simplifier rules: abs-abs: ⊦ j ≠ 0 → abs(abs(j) - 1) = abs(j) - 1; from specification int-abs