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Proof step 4 from proof mkDecimal-maxScale-nle (previous step)

abs(j) < maxScale(i) ⊦ mkDecimal(i, j).int = mkDecimal(i / 10 ^ abs(j), 0).int ∧ mkDecimal(i, j).scale = mkDecimal(i / 10 ^ abs(j), 0).scale

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = 0
Proof step 6:
¬ maxScale(i) ≤ abs(j), abs(j) < maxScale(i) ⊦ mkDecimal(i, j).int = mkDecimal(i / 10 ^ abs(j), 0).int ∧ 0 = mkDecimal(i / 10 ^ abs(j), 0).scale

Rule argument

spec: inst: name: mkDecimal-maxScale-nle-scale seq: ⊦ ¬ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = 0 subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: j, i