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Proof step 28 from proof ushort-band-01 (previous step)

¬ j0 < 0, j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, abs(j0) < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j, ¬ i0 < ~255 ∧ ¬ j0 < ~255

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
j + i * 256 = 255 + (i0 + 255) * 256, j < 256, 0 ≤ i, 0 ≤ j, j + i * 256 < 65535, i0 < ~255, i0 < 0 ⊦ 255 = j

Rule argument

Additional information

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