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Proof step 31 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ 0 ≤ i ∧ 127 < i % 256 → b2i(i2b(i)) = i % 256 - 256
Proof step 33:
¬(0 ≤ ~ i ∧ 127 < ~ i % 256), ~128 ≤ ~(i % 256) ∧ ~(i % 256) ≤ 127, ~128 ≤ i % 256, i < ~128, i < 0, i < i % 256 ⊦ b2i(i2b(~ i)) = ~(i % 256)

Rule argument

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

Additional information

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