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Proof step 56 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 57:
⊦ i < 0 ∧ ~128 ≤ i % 256 → b2i(i2b(i)) = i % 256

Rule argument

name: bib-neg-high rotate: F subst: [i] → [~ i]

Additional information

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