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Proof step 42 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 ∧ ¬ 256 ≤ abs(j0 - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ j < 0 → abs(j) = 0 - j
Proof step 44:
j0 - 1 < 0, 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 ∧ ¬ 256 ≤ 0 - (j0 - 1)

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j0 - 1] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: j0 - 1