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Proof step 3 from proof mkDecimal-maxScale-le-int (previous step)

maxScale(i) ≤ abs(j), ∀ i0, j. i→n(i0) < i→n(i) → maxScale(i0) ≤ abs(j) → mkDecimal(i0, j).int = i0 / 10 ^ maxScale(i0) ⊦ mkDecimal(i, j).int = i / 10 ^ maxScale(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0 → mkDecimal(i, j).int = mkDecimal(i / 10, abs(j) - 1).int
Proof step 5:
¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0), maxScale(i) ≤ abs(j), ∀ i0, j. i→n(i0) < i→n(i) → maxScale(i0) ≤ abs(j) → mkDecimal(i0, j).int = i0 / 10 ^ maxScale(i0) ⊦ mkDecimal(i, j).int = i / 10 ^ maxScale(i)
Proof step 8:
i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0, maxScale(i) ≤ abs(j), ∀ i0, j. i→n(i0) < i→n(i) → maxScale(i0) ≤ abs(j) → mkDecimal(i0, j).int = i0 / 10 ^ maxScale(i0) ⊦ mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ maxScale(i)

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, i] flags: rewrite, current

Additional information

Used terms: j, i