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Proof step 12 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 0 ≤ i ∧ 127 < i % 256 → b2i(i2b(i)) = i % 256 - 256
Proof step 14:
0 ≤ ~ i ∧ 127 < ~ i % 256, i % 256 < ~128, i < 0, i < ~128 ⊦ ~ i % 256 - 256 = b2i(i2b(~(i % 256))), i % 256 = 0

Rule argument

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

Additional information

Used simplifier rules: byte-equal: ⊦ b2i(byi) = b2i(byj) ↔ byi = byj;% ⊦ 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 ↔ i + j < 0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0); Used terms: ~ i