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Proof step 45 from proof ushort-band-shift (previous step)

s2i(sho) = 256 * (i * 256 + j0 - 1), i * 256 + j0 < 0, i ≤ 0, ~255 ≤ i * 256 + j0, ~256 < j0, j0 < 0 ⊦ 255 + j0 = (256 * (i + 1) + j0 - 1) % 256, i ≠ 0 ∧ ¬ j0 ≤ ~255

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ i < j ↔ i +1 = j ∨ i +1 < j
Proof step 47:
s2i(sho) = 256 * (i * 256 + j0 - 1), i * 256 + j0 < 0, i ≤ 0, ~255 ≤ i * 256 + j0, ~256 +1 = j0 ∨ ~256 +1 < j0, j0 < 0 ⊦ 255 + j0 = (256 * (i + 1) + j0 - 1) % 256, i ≠ 0 ∧ ¬ j0 ≤ ~255

Rule argument

seq: ⊦ i < j ↔ i +1 = j ∨ i +1 < j subst: [j, i] → [j0, ~256] rotate: F spec: int-basic1 inst: name: lsrec

Additional information

Used terms: j0, ~256