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Proof step 44 from proof ushort-band-shift (previous step)

j0 - 1 < 0, 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 ≤ 0 - (j0 - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
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 ∧ ¬ j0 ≤ ~255

Rule argument

Additional information

Used simplifier rules: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + ~ j = i - j;% ⊦ ~(i - 1) = ~ i + 1;% ⊦ 0 - i = ~ i;% ⊦ i + j = j + i;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i - j < i0 ↔ i < j + i0;