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Proof step 72 from proof ushort-band-shift (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 73:
s2i(sho) = i * 256 + j, j < 0, i ≤ 0, ~256 < j, s2i(sho) < 0, ~65536 ≤ s2i(sho), 0 ≤ (65536 + s2i(sho)) / 256 ⊦ 255 + i % 256 = ((65536 + s2i(sho)) / 256) % 256, j = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;