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Proof step 1 from proof band-011x (conclusion)

⊦ abs(band(255, b2i(by))) = band(255, b2i(by))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ j < 0 → abs(j) = j

Rule argument

seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [band(255, b2i(by))] rotate: F spec: int-abs inst: name: Abs-pos

Additional information

Used simplifier rules: byte-011x-pos-02: 0 ≤ i, i < 128 ⊦ band(b2i(by), 255) = (* i) ↔ b2i(by) = i;% ⊦ band(i, j) = band(j, i);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i = j ↔ i + j = 0;% ⊦ i + i = 2 * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 2 * i = 0 ↔ i = 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0; Used terms: band(255, b2i(by))