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Proof step 10 from proof fits-law-bxor-01 (previous step)

⊦ bor(band(s2i(sho1), bcompl(b2i(by2))), band(bcompl(s2i(sho1)), b2i(by2))) = s2i(i2s(bor(band(s2i(sho1), bcompl(b2i(by2))), band(bcompl(s2i(sho1)), b2i(by2))))), s2i(i2s(band(s2i(sho1), bcompl(b2i(by2))))) = band(s2i(sho1), bcompl(b2i(by2))) ∧ s2i(i2s(band(bcompl(s2i(sho1)), b2i(by2)))) = band(bcompl(s2i(sho1)), b2i(by2))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i ∈short ∧ j ∈short → s2i(i2s(band(i, j))) = band(i, j)
Proof step 12:
¬(s2i(sho1) ∈short ∧ bcompl(b2i(by2)) ∈short) ⊦ bor(band(s2i(sho1), bcompl(b2i(by2))), band(bcompl(s2i(sho1)), b2i(by2))) = s2i(i2s(bor(band(s2i(sho1), bcompl(b2i(by2))), band(bcompl(s2i(sho1)), b2i(by2))))), s2i(i2s(band(s2i(sho1), bcompl(b2i(by2))))) = band(s2i(sho1), bcompl(b2i(by2))) ∧ s2i(i2s(band(bcompl(s2i(sho1)), b2i(by2)))) = band(bcompl(s2i(sho1)), b2i(by2))
Proof step 17:
s2i(sho1) ∈short ∧ bcompl(b2i(by2)) ∈short ⊦ bor(band(s2i(sho1), bcompl(b2i(by2))), band(bcompl(s2i(sho1)), b2i(by2))) = s2i(i2s(bor(band(s2i(sho1), bcompl(b2i(by2))), band(bcompl(s2i(sho1)), b2i(by2))))), band(s2i(sho1), bcompl(b2i(by2))) = band(s2i(sho1), bcompl(b2i(by2))) ∧ s2i(i2s(band(bcompl(s2i(sho1)), b2i(by2)))) = band(bcompl(s2i(sho1)), b2i(by2))

Rule argument

name: band-sis rotate: F subst: [j, i] → [bcompl(b2i(by2)), s2i(sho1)]

Additional information

Used terms: bcompl(b2i(by2)), s2i(sho1)