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Proof step 16 from proof fits-law-band-01 (previous step)

32768 ≤ band(s2i(sho1), b2i(by2)), 0 < band(s2i(sho1), b2i(by2)), 0 ≤ band(s2i(sho1), b2i(by2)) ⊦ band(s2i(sho1), b2i(by2)) = s2i(i2s(band(s2i(sho1), b2i(by2))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 0 ≤ i ∧ i < i0 → ¬ i0 ≤ band(i, j)
Proof step 18:
¬(0 ≤ s2i(sho1) ∧ s2i(sho1) < 32768), 32768 ≤ band(s2i(sho1), b2i(by2)), 0 < band(s2i(sho1), b2i(by2)), 0 ≤ band(s2i(sho1), b2i(by2)) ⊦ band(s2i(sho1), b2i(by2)) = s2i(i2s(band(s2i(sho1), b2i(by2))))

Rule argument

seq: ⊦ 0 ≤ i ∧ i < i0 → ¬ i0 ≤ band(i, j) subst: [j, i, i0] → [b2i(by2), s2i(sho1), 32768] rotate: F spec: intops inst: name: band-max-05

Additional information

Used terms: b2i(by2), s2i(sho1), 32768