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Proof step 50 from proof getShort-isi (previous step)

32767 < b2i(byi) * 256 + band(b2i(byj), 255) ∧ b2i(byi) * 256 + band(b2i(byj), 255) < b2i(byi) * 256 + 256 → 32767 +1 < b2i(byi) * 256 + 256, 0 < b2i(byi) * 256 + band(b2i(byj), 255), 0 ≤ band(b2i(byj), 255), band(b2i(byj), 255) < 256, 32767 < b2i(byi) * 256 + band(b2i(byj), 255), 0 ≤ b2i(byi) ⊦ 32768 < b2i(byi) * 256 + 256

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 1

Additional information

Used simplifier rules: byte-gr-127: ⊦ ¬ 127 < b2i(by);% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;