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Proof step 10 from proof eq-same (previous step)

mkDecimal(i, j).scale = mkDecimal(i0, j).scale, mkDecimal(i, j).int = mkDecimal(i0, j).int, ∀ 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, i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j)
Proof step 12:
¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0), abs(j) = mkDecimal(i0, j).scale, mkDecimal(i, j).int = mkDecimal(i0, j).int, ∀ 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, i % 10 = 0 ∧ j ≠ 0

Rule argument

spec: inst: name: scale-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j) subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i