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Proof step 13 from proof bib-neg-low (previous step)

¬(j < 0 ∧ 0 < 8 ∧ 2 ^ (8 - 1) < abs(j) ∧ abs(j) < 2 ^ 8 ∧ i0 < 0), j < ~128, i0 * 2 ^ 8 + j < ~128, ~256 < j, i0 ≤ 0, j < 0, i0 * 2 ^ 8 + j < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i0 * 2 ^ 8 + j))))) = j + 2 ^ 8

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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