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Proof step 78 from proof ushort-band-shift (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 79:
0 ≤ (256 * (i + 256) + j) / 256, i * 256 + j < 0, ~256 < i, ~65536 ≤ i * 256 + j, ~256 < j, i ≤ 0, j < 0 ⊦ j = 0, 255 + i % 256 = ((256 * (i + 256) + j) / 256) % 256

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i < j → ¬ j < i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;