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Proof step 9 from proof modex-odd-neg (previous step)

2 * j = (i0 * 2 + j0) + 1, i0 * 2 + j0 < 0, abs(j0) < 2, j ≤ 0, j0 ≤ 0, i0 ≤ 0 ⊦ j0 = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs name: Abs-neg seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 0 - i = ~ i; (s)% ⊦ ~ i < j ↔ 0 < j + i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ i < 0 → (~2 < i ↔ i = ~1); (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ ¬ j < 0 → abs(j) = j; (s)%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)% ⊦ 2 * i + 1 ≠ 2 * j; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j0