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Proof step 9 from proof ushort-band-01 (previous step)

s2i(sho) + 65536 = i * 256 + j, 0 ≤ i, 0 ≤ j, ~65536 ≤ s2i(sho), s2i(sho) < 0, j < 256 ⊦ (s2i(sho) + 1) % 256 + 255 = j

User applied rule cut formula

And obtained the following new goals

Proof step 10:
s2i(sho) = i * 256 + j - 65536, s2i(sho) + 65536 = i * 256 + j, 0 ≤ i, 0 ≤ j, ~65536 ≤ s2i(sho), s2i(sho) < 0, j < 256 ⊦ (s2i(sho) + 1) % 256 + 255 = j

Rule argument

fma: s2i(sho) = i * 256 + j - 65536

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; Used formulas: s2i(sho) = i * 256 + j - 65536