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Proof step 30 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 - 1) + fillsgn(i→n(8), int2bits(j).rest))))) = j + 2 ^ 8

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
j < ~128, 256 * i0 + j < ~128, ~256 < j, j < 0, 256 * i0 + j < 0, i0 < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i0 - 1) + fillsgn(8, int2bits(j).rest))))) = 256 + j

Rule argument

Additional information

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