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Proof step 9 from proof scale-negate (previous step)

∀ i0, j. i→n(i0) < i→n(i) → true → mkDecimal(~ i0, j).scale = mkDecimal(i0, j).scale ⊦ mkDecimal(~ i, j).scale = abs(j), i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0, i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j)

Rule argument

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

Additional information

Used simplifier rules: mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j); from specification int-div%neg-10: ⊦ ~ i = 0 ↔ i = 0; from specification int-abs Used terms: j, ~ i