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Proof step 18 from proof fits-law-bxor-01 (previous step)

~32768 ≤ bcompl(b2i(by2)), bcompl(b2i(by2)) ≤ 32767 ⊦ 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(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 19:
⊦ i ∈short ∧ j ∈short → s2i(i2s(band(i, j))) = band(i, j)
Proof step 20:
¬(bcompl(s2i(sho1)) ∈short ∧ b2i(by2) ∈short), ~32768 ≤ bcompl(b2i(by2)), bcompl(b2i(by2)) ≤ 32767 ⊦ 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(bcompl(s2i(sho1)), b2i(by2)))) = band(bcompl(s2i(sho1)), b2i(by2))

Rule argument

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

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i); Used terms: b2i(by2), bcompl(s2i(sho1))