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Proof step 34 from proof ushort-band-shift (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 35:
256 + i * 256 + (j0 - 1) = 256 * (i + 1) + (j0 - 1), 1 + i * 256 + (j0 - 1) = i * 256 + j0, s2i(sho) = (i * 256 + (j0 - 1)) * 256, i * 256 + (j0 - 1) < 0, ~256 ≤ i * 256 + (j0 - 1), abs(j0) < 256, i * 256 + (j0 - 1) < ~1, j0 ≤ 0, i ≤ 0 ⊦ 255 + j0 = (256 + i * 256 + (j0 - 1)) % 256

Rule argument

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

Additional information

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