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Proof step 10 from proof mkDecimal-maxScale-nle (previous step)

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

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 ^ abs(j)) % 10 = 0 ∧ 0 ≠ 0 ∧ i / 10 ^ abs(j) ≠ 0), abs(j) < maxScale(i) ⊦ i / 10 ^ abs(j) = mkDecimal(i / 10 ^ abs(j), 0).int ∧ 0 = abs(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] → [0, i / 10 ^ abs(j)] flags: rewrite, current

Additional information

Used terms: 0, i / 10 ^ abs(j)