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Proof step 29 from proof ushort-band-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 30:
255 + (i0 + 255) * 256 < 0, j + i * 256 = 255 + (i0 + 255) * 256, j < 256, 0 ≤ i, 0 ≤ j, j + i * 256 < 65535, i0 < ~255, i0 < 0 ⊦ 255 = j

Rule argument

fma: 255 + (i0 + 255) * 256 < 0

Additional information

Used simplifier rules: ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used formulas: 255 + (i0 + 255) * 256 < 0