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Proof step 41 from proof ushort-band-shift (previous step)

j0 < 0, s2i(sho) = 256 * (i * 256 + j0 - 1), j0 ≤ 0, i ≤ 0, ~255 ≤ i * 256 + j0, 0 - j0 < 256, i * 256 + j0 < 0 ⊦ 255 + j0 = (256 * (i + 1) + j0 - 1) % 256, i ≠ 0 ∧ ¬ 256 ≤ abs(j0 - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
s2i(sho) = 256 * (i * 256 + j0 - 1), i * 256 + j0 < 0, i ≤ 0, ~255 ≤ i * 256 + j0, ~256 < j0, j0 < 0 ⊦ 255 + j0 = (256 * (i + 1) + j0 - 1) % 256, i ≠ 0 ∧ ¬ 256 ≤ abs(j0 - 1)

Rule argument

Additional information

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