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Proof step 29 from proof ushort-band-shift (previous step)

s2i(sho) = j * 256, j < 0, ~256 ≤ j, 0 ≤ (256 * (256 + j)) / 256 ⊦ 255 + (1 + j) % 256 = ((256 * (256 + j)) / 256) % 256

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
s2i(sho) = j * 256, j < 0, ~256 ≤ j ⊦ 255 + (1 + j) % 256 = (256 + j) % 256

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;%j ≠ 0 ⊦ (i * j) / j = i;