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Proof step 16 from proof eq-same (previous step)

abs(j) = mkDecimal(i0, j).scale, ∀ i1, i2, j0. i→n(i1) + i→n(i2) < i→n(mkDecimal(i0, j).int) + i→n(i0) → mkDecimal(i1, j0).scale = mkDecimal(i2, j0).scale ∧ mkDecimal(i1, j0).int = mkDecimal(i2, j0).int → i1 = i2 ⊦ mkDecimal(i0, j).int = i0, mkDecimal(i0, j).int % 10 = 0 ∧ j ≠ 0, mkDecimal(i0, j).int % 10 = 0 ∧ j ≠ 0 ∧ mkDecimal(i0, j).int ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0 → mkDecimal(i, j).int = mkDecimal(i / 10, abs(j) - 1).int
Proof step 18:
¬(i0 % 10 = 0 ∧ j ≠ 0 ∧ i0 ≠ 0), abs(j) = mkDecimal(i0, j).scale, ∀ i1, i2, j0. i→n(i1) + i→n(i2) < i→n(mkDecimal(i0, j).int) + i→n(i0) → mkDecimal(i1, j0).scale = mkDecimal(i2, j0).scale ∧ mkDecimal(i1, j0).int = mkDecimal(i2, j0).int → i1 = i2 ⊦ mkDecimal(i0, j).int = i0, mkDecimal(i0, j).int % 10 = 0 ∧ j ≠ 0, mkDecimal(i0, j).int % 10 = 0 ∧ j ≠ 0 ∧ mkDecimal(i0, j).int ≠ 0
Proof step 24:
i0 % 10 = 0 ∧ j ≠ 0 ∧ i0 ≠ 0, abs(j) = mkDecimal(i0, j).scale, ∀ i1, i2, j0. i→n(i1) + i→n(i2) < i→n(mkDecimal(i0 / 10, abs(j) - 1).int) + i→n(i0) → mkDecimal(i1, j0).scale = mkDecimal(i2, j0).scale ∧ mkDecimal(i1, j0).int = mkDecimal(i2, j0).int → i1 = i2 ⊦ mkDecimal(i0 / 10, abs(j) - 1).int = i0, mkDecimal(i0 / 10, abs(j) - 1).int % 10 = 0 ∧ j ≠ 0, mkDecimal(i0 / 10, abs(j) - 1).int % 10 = 0 ∧ j ≠ 0 ∧ mkDecimal(i0 / 10, abs(j) - 1).int ≠ 0

Rule argument

spec: inst: name: intvalue-rec seq: ⊦ i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0 → mkDecimal(i, j).int = mkDecimal(i / 10, abs(j) - 1).int subst: [j, i] → [j, i0] flags: rewrite, current

Additional information

Used terms: j, i0