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Proof step 3 from proof mkDecimal-maxScale-nle-scale (previous step)

abs(j) < maxScale(i), ∀ i0, j. i→n(i0) < i→n(i) → abs(j) < maxScale(i0) → mkDecimal(i0, j).scale = 0 ⊦ mkDecimal(i, j).scale = 0

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

Rule argument

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

Additional information

Used terms: j, i