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Proof step 14 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ 127 < i ∧ i < 256 → b2i(i2b(i)) = i - 256

Rule argument

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

Additional information

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