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Proof step 19 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ ~128 ≤ i ∧ i ≤ 127 → b2i(i2b(i)) = i
Proof step 21:
¬(~128 ≤ ~(i % 256) ∧ ~(i % 256) ≤ 127), ~128 ≤ i % 256, i < ~128, i < 0, i < i % 256 ⊦ b2i(i2b(~ i)) = b2i(i2b(~(i % 256)))
Proof step 31:
~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-in-01 rotate: F subst: [i] → [~(i % 256)]

Additional information

Used terms: ~(i % 256)