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Proof step 18 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ i ∈byte ∧ j ∈byte → b2i(i2b(band(i, j))) = band(i, j)
Proof step 20:
¬(bcompl(b2i(by1)) ∈byte ∧ b2i(by2) ∈byte), ~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))

Rule argument

name: band-bib rotate: F subst: [j, i] → [b2i(by2), bcompl(b2i(by1))]

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i); Used terms: b2i(by2), bcompl(b2i(by1))