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Proof step 45 from proof equality-any (previous step)

¬(0 < 10 ∧ 0 ≤ abs(j0) ∧ abs(j0) ≤ abs(j)), i * 10 ^ abs(j0) = i0 * 10 ^ abs(j), ∀ 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)) ⊦ i = i0 ∧ abs(j) = abs(j0), i % 10 = 0, i0 % 10 = 0, i = 0, i0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
i * 10 ^ abs(j0) = i0 * 10 ^ abs(j), abs(j) < abs(j0), ∀ 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)) ⊦ i % 10 = 0, i0 % 10 = 0, i = 0, i0 = 0, i = i0 ∧ abs(j) = abs(j0)

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%abs-03: ⊦ 0 ≤ abs(i); from specification int-abs