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Proof step 48 from proof getShort-isi (previous step)

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 insert spec-lemma

And obtained the following new goals

Proof step 49:
⊦ i < j ∧ j < i0 → i +1 < i0
Proof step 50:
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

Rule argument

seq: ⊦ i < j ∧ j < i0 → i +1 < i0 subst: [i, j, i0] → [32767, b2i(byi) * 256 + band(b2i(byj), 255), b2i(byi) * 256 + 256] rotate: F spec: int-basic1 inst: name: lf-01

Additional information

Used terms: 32767, b2i(byi) * 256 + band(b2i(byj), 255), b2i(byi) * 256 + 256