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Proof step 49 from proof byte-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ i < 0 ∧ i % 256 < ~128 → b2i(i2b(i)) = i % 256 + 256
Proof step 51:
¬(~ i < 0 ∧ ~ i % 256 < ~128), 0 < i % 256, 127 < i, 0 ≤ i, 0 < i, 127 < i % 256 ⊦ b2i(i2b(~ i)) = b2i(i2b(256 - i % 256))
Proof step 58:
~ i < 0 ∧ ~ i % 256 < ~128, 0 < i % 256, 127 < i, 0 ≤ i, 0 < i, 127 < i % 256 ⊦ ~ i % 256 + 256 = b2i(i2b(256 - i % 256))

Rule argument

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

Additional information

Used terms: ~ i