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Proof step 12 from proof fits-law-band-01 (previous step)

band(s2i(sho1), b2i(by2)) < ~32768, band(s2i(sho1), b2i(by2)) < 0, s2i(sho1) < 0, b2i(by2) < 0 ⊦ 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 13:
⊦ i0 ≤ ~(2 ^ (n→i(# int2bits(i)) - 1)) ∧ i0 ≤ ~(2 ^ (n→i(# int2bits(j)) - 1)) → ¬ band(i, j) < i0
Proof step 14:
¬(~32768 ≤ ~(2 ^ (n→i(# int2bits(s2i(sho1))) - 1)) ∧ ~32768 ≤ ~(2 ^ (n→i(# int2bits(b2i(by2))) - 1))), band(s2i(sho1), b2i(by2)) < ~32768, band(s2i(sho1), b2i(by2)) < 0, s2i(sho1) < 0, b2i(by2) < 0 ⊦ band(s2i(sho1), b2i(by2)) = s2i(i2s(band(s2i(sho1), b2i(by2))))

Rule argument

seq: ⊦ i0 ≤ ~(2 ^ (n→i(# int2bits(i)) - 1)) ∧ i0 ≤ ~(2 ^ (n→i(# int2bits(j)) - 1)) → ¬ band(i, j) < i0 subst: [i0, j, i] → [~32768, b2i(by2), s2i(sho1)] rotate: F spec: intops inst: name: band-min-02

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i); Used terms: ~32768, b2i(by2), s2i(sho1)