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Proof step 8 from proof fits-law-bor-02 (previous step)

⊦ bcompl(band(bcompl(s2i(sho1)), bcompl(s2i(sho2)))) = s2i(i2s(bcompl(band(bcompl(s2i(sho1)), bcompl(s2i(sho2)))))), s2i(i2s(band(bcompl(s2i(sho1)), bcompl(s2i(sho2))))) = band(bcompl(s2i(sho1)), bcompl(s2i(sho2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i ∈short ∧ j ∈short → s2i(i2s(band(i, j))) = band(i, j)
Proof step 10:
¬(bcompl(s2i(sho1)) ∈short ∧ bcompl(s2i(sho2)) ∈short) ⊦ bcompl(band(bcompl(s2i(sho1)), bcompl(s2i(sho2)))) = s2i(i2s(bcompl(band(bcompl(s2i(sho1)), bcompl(s2i(sho2)))))), s2i(i2s(band(bcompl(s2i(sho1)), bcompl(s2i(sho2))))) = band(bcompl(s2i(sho1)), bcompl(s2i(sho2)))

Rule argument

name: band-sis rotate: F subst: [j, i] → [bcompl(s2i(sho2)), bcompl(s2i(sho1))]

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i); Used terms: bcompl(s2i(sho2)), bcompl(s2i(sho1))