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Proof step 9 from proof getint-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: neg-03: ⊦ ~ i + i = 0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%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