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Proof step 45 from proof getShort-isi (previous step)

band(b2i(byj), 255) < 256, 0 ≤ band(b2i(byj), 255), 0 ≤ b2i(byi) ⊦ ¬ b2i(byi) * 256 + band(b2i(byj), 255) < ~32768 ∧ ¬ 32767 < b2i(byi) * 256 + band(b2i(byj), 255)

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information

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