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Proof step 97 from proof ushort-band-shift (previous step)

j0 = (i * 256 - 255) + j1, 255 + j0 = i * 256 + j1, 0 ≤ i, 0 ≤ j1, 256 * j0 + j < 0, j0 < 0, ~255 ≤ j0, ~256 ≤ j, j < 0, ~256 < j, ~65536 ≤ 256 * j0 + j, j1 < 256 ⊦ i = 0, 255 + j0 = j1, j = 0

User applied rule cut formula

And obtained the following new goals

Proof step 98:
i * 256 - 255 = (i - 1) * 256 + 1, j0 = (i * 256 - 255) + j1, 255 + j0 = i * 256 + j1, 0 ≤ i, 0 ≤ j1, 256 * j0 + j < 0, j0 < 0, ~255 ≤ j0, ~256 ≤ j, j < 0, ~256 < j, ~65536 ≤ 256 * j0 + j, j1 < 256 ⊦ i = 0, 255 + j0 = j1, j = 0

Rule argument

fma: i * 256 - 255 = (i - 1) * 256 + 1

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0); Used formulas: i * 256 - 255 = (i - 1) * 256 + 1