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Proof step 8 from proof bib-neg-low (previous step)

i = i0 * 256 + j ∧ j ≤ 0 ∧ abs(j) < 256 ∧ i0 ≤ 0 ∧ 0 < 256, i < ~128, j < ~128, i < 0, j < 0, i < ~128 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i))))) = j + 256

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j < ~128, i0 * 256 + j < ~128, ~256 < j, i0 ≤ 0, j < 0, i0 * 256 + j < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i0 * 256 + j))))) = j + 256

Rule argument

Additional information

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