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Proof step 21 from proof fits-law-bxor (previous step)

~128 ≤ bcompl(b2i(by2)), bcompl(b2i(by2)) ≤ 127 ⊦ bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))) = b2i(i2b(bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))))), b2i(i2b(band(bcompl(b2i(by1)), b2i(by2)))) = band(bcompl(b2i(by1)), b2i(by2)), bcompl(b2i(by1)) ∈byte

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ i ∈byte ↔ b2i(i2b(i)) = i
Proof step 23:
~128 ≤ bcompl(b2i(by2)), bcompl(b2i(by2)) ≤ 127 ⊦ bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))) = b2i(i2b(bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))))), b2i(i2b(band(bcompl(b2i(by1)), b2i(by2)))) = band(bcompl(b2i(by1)), b2i(by2)), b2i(i2b(bcompl(b2i(by1)))) = bcompl(b2i(by1))

Rule argument

name: inbyte-bib rotate: F subst: [i] → [bcompl(b2i(by1))]

Additional information

Used terms: bcompl(b2i(by1))