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Proof step 83 from proof ushort-band-shift (previous step)

0 < 256 ∧ 0 ≤ i + 255 ∧ 0 ≤ 256 + j ∧ 256 + j < 256, 0 ≤ i + 255, i * 256 + j < 0, ~256 < i, ~65536 ≤ i * 256 + j, ~256 < j, i ≤ 0, j < 0 ⊦ j = 0, 255 + i % 256 = (i + 255) % 256

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 84:
i * 256 + j < 0, ~65536 ≤ i * 256 + j, ~256 < j, i ≤ 0, j < 0, ~256 ≤ j, ~255 ≤ i ⊦ j = 0, 255 + i % 256 = (i + 255) % 256

Rule argument

Additional information

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