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Proof step 8 from proof fits-law-bor (previous step)

⊦ bcompl(band(bcompl(b2i(by1)), bcompl(b2i(by2)))) = b2i(i2b(bcompl(band(bcompl(b2i(by1)), bcompl(b2i(by2)))))), b2i(i2b(band(bcompl(b2i(by1)), bcompl(b2i(by2))))) = band(bcompl(b2i(by1)), bcompl(b2i(by2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i ∈byte ∧ j ∈byte → b2i(i2b(band(i, j))) = band(i, j)
Proof step 10:
¬(bcompl(b2i(by1)) ∈byte ∧ bcompl(b2i(by2)) ∈byte) ⊦ bcompl(band(bcompl(b2i(by1)), bcompl(b2i(by2)))) = b2i(i2b(bcompl(band(bcompl(b2i(by1)), bcompl(b2i(by2)))))), b2i(i2b(band(bcompl(b2i(by1)), bcompl(b2i(by2))))) = band(bcompl(b2i(by1)), bcompl(b2i(by2)))

Rule argument

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

Additional information

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