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Proof step 86 from proof ushort-band-shift (previous step)

abs(j0) < 256, ~65536 ≤ (i0 * 256 + j0) * 256 + j, ~256 < j, j < 0, ~256 ≤ j, ~255 ≤ i0 * 256 + j0, j0 ≤ 0, i0 ≤ 0, i0 * 256 + j0 < 0, (i0 * 256 + j0) * 256 + j < 0 ⊦ j = 0, 255 + j0 = ((i0 * 256 + j0) + 255) % 256

User applied rule cut formula

And obtained the following new goals

Proof step 87:
(i0 * 256 + j0) + 255 = 256 * (i0 + 1) + (j0 - 1), abs(j0) < 256, ~65536 ≤ (i0 * 256 + j0) * 256 + j, ~256 < j, j < 0, ~256 ≤ j, ~255 ≤ i0 * 256 + j0, j0 ≤ 0, i0 ≤ 0, i0 * 256 + j0 < 0, (i0 * 256 + j0) * 256 + j < 0 ⊦ j = 0, 255 + j0 = ((i0 * 256 + j0) + 255) % 256

Rule argument

fma: (i0 * 256 + j0) + 255 = 256 * (i0 + 1) + (j0 - 1)

Additional information

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