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Proof step 14 from proof short-2bytes (previous step)

band(b2i(by0), 255) + 256 * ~128 = ~32768 ∨ ~32768 < band(b2i(by0), 255) + 256 * ~128, band(b2i(by0), 255) + 256 * b2i(by) < ~32768 ⊦

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 1

Additional information

Used simplifier rules: i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;%0 ≤ i, i < 128 ⊦ band(b2i(by), 255) = (* i) ↔ b2i(by) = i;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ 0 ≤ i → band(i, 255) = i % 256;% ⊦ i + 0 = i;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i);% ⊦ ¬ b2i(by) < ~128;