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Proof step 6 from proof byte-mult-neg (previous step)

¬(i * 256 + j < 0 ∧ ~128 ≤ (i * 256 + j) % 256), i < 0, j < 0 ⊦ b2i(i2b(i * 256 + j)) = b2i(i2b(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i < 0 ∧ i % 256 < ~128 → b2i(i2b(i)) = i % 256 + 256
Proof step 8:
¬(i * 256 + j < 0 ∧ (i * 256 + j) % 256 < ~128), ¬(i * 256 + j < 0 ∧ ~128 ≤ (i * 256 + j) % 256), i < 0, j < 0 ⊦ b2i(i2b(i * 256 + j)) = b2i(i2b(j))
Proof step 13:
i * 256 + j < 0 ∧ (i * 256 + j) % 256 < ~128, ¬(i * 256 + j < 0 ∧ ~128 ≤ (i * 256 + j) % 256), i < 0, j < 0 ⊦ (i * 256 + j) % 256 + 256 = b2i(i2b(j))

Rule argument

name: bib-neg-low rotate: F subst: [i] → [i * 256 + j]

Additional information

Used terms: i * 256 + j