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Proof step 26 from proof ushort-band-01 (previous step)

j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, abs(j0) < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j, ¬ i0 < ~255 ∧ ¬ j0 < ~255

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ j < 0 → abs(j) = 0 - j
Proof step 28:
¬ j0 < 0, j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, abs(j0) < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j, ¬ i0 < ~255 ∧ ¬ j0 < ~255
Proof step 31:
j0 < 0, j + i * 256 = (i0 + 255) * 256 + j0 + 255, i0 ≤ 0, j0 ≤ 0, j + i * 256 < 65535, 0 - j0 < 256, 0 ≤ j, 0 ≤ i, j < 256 ⊦ 255 + j0 = j, ¬ i0 < ~255 ∧ ¬ j0 < ~255

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j0] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used terms: j0