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Proof step 14 from proof ushort-band-01 (previous step)

0 < j + i * 256, 65535 ≤ j + i * 256, i * 256 + j < 65536, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + (j + i * 256 - 65535) % 256 = j

User applied rule cut formula

And obtained the following new goals

Proof step 15:
i * 256 + j ≤ 65535, 0 < j + i * 256, 65535 ≤ j + i * 256, i * 256 + j < 65536, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + (j + i * 256 - 65535) % 256 = j

Rule argument

fma: i * 256 + j ≤ 65535

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i ≠ j → (i ≤ j ↔ i < j);%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used formulas: i * 256 + j ≤ 65535