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Proof step 10 from proof test-div-01 (previous step)

⊦ mkDecimal (10 ^ (mkDecimal(3, 0).scale + 4) / mkDecimal(3, 0).int / 10 ^ maxScale(mkDecimal(3, 0).int), mkDecimal(1, 0).scale + 4 + maxScale(mkDecimal(3, 0).int)) = mkDecimal(3333, 4), mkDecimal(3, 0) | mkDecimal(1, 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:
¬(3 % 10 = 0 ∧ 0 ≠ 0 ∧ 3 ≠ 0) ⊦ mkDecimal(10 ^ (abs(0) + 4) / mkDecimal(3, 0).int / 10 ^ maxScale(mkDecimal(3, 0).int), mkDecimal(1, 0).scale + 4 + maxScale(mkDecimal(3, 0).int)) = mkDecimal(3333, 4), mkDecimal(3, 0) | mkDecimal(1, 0)

Rule argument

spec: decimal inst: name: scale-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j) subst: [j, i] → [0, 3] flags: rewrite

Additional information

Used terms: 0, 3