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Proof step 7 from proof eq-same (previous step)

mkDecimal(i, j).int = mkDecimal(i0, j).int, mkDecimal(i, j).scale = mkDecimal(i0, j).scale, ∀ 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 = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1)
Proof step 9:
¬(i % 10 = 0 ∧ j ≠ 0), mkDecimal(i, j).int = mkDecimal(i0, j).int, mkDecimal(i, j).scale = mkDecimal(i0, j).scale, ∀ 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 = i0
Proof step 28:
i % 10 = 0 ∧ j ≠ 0, mkDecimal(i / 10, abs(j) - 1).int = mkDecimal(i0, j).int, mkDecimal(i / 10, abs(j) - 1).scale = mkDecimal(i0, j).scale, ∀ 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 = i0

Rule argument

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

Additional information

Used terms: j, i