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Proof step 51 from proof ushort-band-shift (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
s2i(sho) = 256 * (j0 - 1), 255 + j0 = i * 256 + j, 0 ≤ i, 0 ≤ j, ~255 < j0, j0 < 0, j < 256 ⊦ ~255 = j0, 255 + j0 = j

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;