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Proof step 59 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ ~128 ≤ i ∧ i ≤ 127 → b2i(i2b(i)) = i

Rule argument

name: bib-in-01 rotate: F subst: [i] → [256 - i % 256]

Additional information

Used simplifier rules: ⊦ i + (j - i) = j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j ≤ i0 ↔ i ≤ j + i0;%j < j0, 0 < j ⊦ i % (* j) ≤ (* j0);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used terms: 256 - i % 256