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Proof step 31 from proof ushort-band-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
j + i * 256 = (i0 + 255) * 256 + j0 + 255, j0 < 0, ~256 < j0, j + i * 256 < 65535, i0 ≤ 0, j < 256, 0 ≤ i, 0 ≤ j ⊦ 255 + j0 = j, ¬ i0 < ~255 ∧ ¬ j0 < ~255

Rule argument

Additional information

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