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Proof step 34 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ 0 ≤ i ∧ i % 256 ≤ 127 → b2i(i2b(i)) = i % 256

Rule argument

name: bib-pos-low rotate: F subst: [i] → [~ i]

Additional information

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