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Proof step 32 from proof ushort-band-shift (previous step)

1 + j = i * 256 + j0, s2i(sho) = j * 256, j < 0, ~256 ≤ j, abs(j0) < 256, j < ~1, j0 ≤ 0, i ≤ 0 ⊦ 255 + j0 = (256 + j) % 256

User applied rule cut formula

And obtained the following new goals

Proof step 33:
j = i * 256 + (j0 - 1), 1 + j = i * 256 + j0, s2i(sho) = j * 256, j < 0, ~256 ≤ j, abs(j0) < 256, j < ~1, j0 ≤ 0, i ≤ 0 ⊦ 255 + j0 = (256 + j) % 256

Rule argument

fma: j = i * 256 + (j0 - 1)

Additional information

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