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Proof step 13 from proof scale-negate (previous step)

mkDecimal(~(i / 10), abs(j) - 1).scale = mkDecimal(i / 10, abs(j) - 1).scale, i % 10 = 0, ∀ i0, j. i→n(i0) < i→n(i) → true → mkDecimal(~ i0, j).scale = mkDecimal(i0, j).scale ⊦ j = 0, mkDecimal(~ i, j).scale = mkDecimal(i / 10, abs(j) - 1).scale

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: mkDecimal-rec seq: ⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1) 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%neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j); from specification int-div Used terms: j, ~ i