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Proof step 4 from proof fits-law-band-02 (previous step)

⊦ band(s2i(sho1), s2i(sho2)) = s2i(i2s(band(s2i(sho1), s2i(sho2)))), ¬ band(s2i(sho1), s2i(sho2)) < ~32768 ∧ ¬ 32768 ≤ band(s2i(sho1), s2i(sho2))

User applied rule case distinction

And obtained the following new goals

Proof step 5:
⊦ ¬ band(s2i(sho1), s2i(sho2)) < ~32768, band(s2i(sho1), s2i(sho2)) = s2i(i2s(band(s2i(sho1), s2i(sho2))))
Proof step 15:
⊦ ¬ 32768 ≤ band(s2i(sho1), s2i(sho2)), band(s2i(sho1), s2i(sho2)) = s2i(i2s(band(s2i(sho1), s2i(sho2))))

Rule argument

pos: right 2

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