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Proof step 85 from proof ushort-band-shift (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 86:
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 = ((i0 * 256 + j0) + 255) % 256

Rule argument

Additional information

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