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Proof step 21 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)), bcompl(s2i(sho1)) ∈short

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ i ∈short ↔ s2i(i2s(i)) = i
Proof step 23:
~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)), s2i(i2s(bcompl(s2i(sho1)))) = bcompl(s2i(sho1))

Rule argument

name: inshort-sis rotate: F subst: [i] → [bcompl(s2i(sho1))]

Additional information

Used terms: bcompl(s2i(sho1))