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Proof step 40 from proof eq-same (previous step)

i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = mkDecimal(i0 / 10, abs(j) - 1).int, mkDecimal(i / 10, abs(j) - 1).scale = mkDecimal(i0 / 10, abs(j) - 1).scale, i0 % 10 = 0, ∀ i1, i2, j. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → mkDecimal(i1, j).scale = mkDecimal(i2, j).scale ∧ mkDecimal(i1, j).int = mkDecimal(i2, j).int → i1 = i2 ⊦ i→n(i / 10) + i→n(i0 / 10) < i→n(i) + i→n(i0), j = 0, i = i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = mkDecimal(i0 / 10, abs(j) - 1).int, mkDecimal(i / 10, abs(j) - 1).scale = mkDecimal(i0 / 10, abs(j) - 1).scale, i0 % 10 = 0, i→n(i) + i→n(i0) ≤ i→n(i / 10) + i→n(i0 / 10), ∀ i1, i2, j. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → mkDecimal(i1, j).scale = mkDecimal(i2, j).scale ∧ mkDecimal(i1, j).int = mkDecimal(i2, j).int → i1 = i2 ⊦ j = 0, i = i0

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat