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

¬ 0 ≤ s2i(sho1), band(s2i(sho1), s2i(sho2)) < ~32768, band(s2i(sho1), s2i(sho2)) < 0 ⊦ band(s2i(sho1), s2i(sho2)) = s2i(i2s(band(s2i(sho1), s2i(sho2))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
band(s2i(sho1), s2i(sho2)) < ~32768, band(s2i(sho1), s2i(sho2)) < 0, s2i(sho1) < 0 ⊦ band(s2i(sho1), s2i(sho2)) = s2i(i2s(band(s2i(sho1), s2i(sho2))))

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;