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Proof step 63 from proof ushort-band-shift (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 64:
0 ≤ i * 256 + j0 + 255, s2i(sho) = 256 * (i * 256 + j0 - 1), j0 ≤ 0, abs(j0 - 1) < 256, ~255 ≤ i * 256 + j0, abs(j0) < 256, i < 0, i * 256 + j0 < 0 ⊦ i = ~1

Rule argument

fma: 0 ≤ i * 256 + j0 + 255

Additional information

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