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Proof step 92 from proof ushort-band-shift (previous step)

i0 = 0, abs(j0) < 256, ~65536 ≤ (i0 * 256 + j0) * 256 + j, ~256 < j, j < 0, ~256 ≤ j, ~255 ≤ i0 * 256 + j0, j0 ≤ 0, i0 ≤ 0, i0 * 256 + j0 < 0, (i0 * 256 + j0) * 256 + j < 0 ⊦ j = 0, 255 + j0 = (256 * (i0 + 1) + j0 - 1) % 256, i0 ≠ 0 ∧ ¬ 256 ≤ abs(j0 - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 93:
~65536 ≤ 256 * j0 + j, ~256 < j, j < 0, ~256 ≤ j, ~255 ≤ j0, j0 < 0, 256 * j0 + j < 0 ⊦ j = 0, 255 + j0 = (255 + j0) % 256

Rule argument

Additional information

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