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Proof step 7 from proof int2bits-mod2-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: ⊦ i < 0 → (~2 < i ↔ i = ~1);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ 0 - i = ~ i;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ¬ j < 0 → abs(j) = j;%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 2 * i ≠ ~1;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: j