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Proof step 102 from proof ushort-band-shift (previous step)

0 < 256 ∧ i0 + 1 ≤ 0 ∧ j0 - 1 ≤ 0 ∧ abs(j0 - 1) < 256, 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 = j0 - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 103:
abs(j0 - 1) < 256, abs(j0) < 256, ~65536 ≤ (i0 * 256 + j0) * 256 + j, ~256 < j, j < 0, ~256 ≤ j, ~255 ≤ i0 * 256 + j0, j0 ≤ 0, i0 * 256 + j0 < 0, (i0 * 256 + j0) * 256 + j < 0, i0 < 0 ⊦ j = 0

Rule argument

Additional information

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