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Proof step 27 from proof ushort-band-shift (previous step)

s2i(sho) = j * 256, j < 0, ~256 ≤ j, 0 ≤ (65536 + j * 256) / 256 ⊦ 255 + (1 + j) % 256 = ((65536 + j * 256) / 256) % 256

User applied rule cut formula

And obtained the following new goals

Proof step 28:
65536 + j * 256 = 256 * (256 + j), s2i(sho) = j * 256, j < 0, ~256 ≤ j, 0 ≤ (65536 + j * 256) / 256 ⊦ 255 + (1 + j) % 256 = ((65536 + j * 256) / 256) % 256

Rule argument

fma: 65536 + j * 256 = 256 * (256 + j)

Additional information

Used simplifier rules: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used formulas: 65536 + j * 256 = 256 * (256 + j)