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Proof step 79 from proof ushort-band-shift (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 80:
256 * (i + 256) + j = 256 * (i + 255) + 256 + j, 0 ≤ (256 * (i + 256) + j) / 256, i * 256 + j < 0, ~256 < i, ~65536 ≤ i * 256 + j, ~256 < j, i ≤ 0, j < 0 ⊦ j = 0, 255 + i % 256 = ((256 * (i + 256) + j) / 256) % 256

Rule argument

fma: 256 * (i + 256) + j = 256 * (i + 255) + 256 + j

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: 256 * (i + 256) + j = 256 * (i + 255) + 256 + j