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Proof step 25 from proof ushort-band-01 (previous step)

¬(0 ≤ i ∧ 0 ≤ i0 + 255 ∧ 0 ≤ j ∧ 0 ≤ 255 + j0 ∧ j < 256 ∧ 255 + j0 < 256), j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, abs(j0) < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, abs(j0) < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j, ¬ i0 < ~255 ∧ ¬ j0 < ~255

Rule argument

Additional information

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