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Proof step 44 from proof byte-law-neg (previous step)

~ i < 0 ∧ ~128 ≤ ~ i % 256, 0 < i, 0 ≤ i, 127 < i, i % 256 ≤ 127, i % 256 < i ⊦ ~ i % 256 = b2i(i2b(~(i % 256)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ i < 0 ∧ ~128 ≤ i % 256 → b2i(i2b(i)) = i % 256

Rule argument

name: bib-neg-high rotate: F subst: [i] → [~(i % 256)]

Additional information

Used simplifier rules: byte: ⊦ b2i(i2b(0)) = 0;% ⊦ ~ i = ~ j ↔ i = j;%j ≠ 0 ⊦ ~ i % j = ~(i % j);% ⊦ ~ i = j ↔ i + j = 0;% ⊦ ~ i < 0 ↔ 0 < i;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j ≤ i0 ↔ i ≤ j + i0;%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i ∧ 0 < j → (i % j ≤ 0 ↔ i % j = 0);%j ≠ 0 ⊦ (i % j) % j = i % j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) Used terms: ~(i % 256)