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Proof step 17 from proof fits-law-bxor-01 (previous step)

s2i(sho1) ∈short ∧ bcompl(b2i(by2)) ∈short ⊦ 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))))), band(s2i(sho1), bcompl(b2i(by2))) = band(s2i(sho1), bcompl(b2i(by2))) ∧ s2i(i2s(band(bcompl(s2i(sho1)), b2i(by2)))) = band(bcompl(s2i(sho1)), b2i(by2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
~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))

Rule argument

Additional information

Used simplifier rules: short2int-in: ⊦ s2i(sho) ∈short;%inshort: ⊦ i ∈short ↔ ~32768 ≤ i ∧ i ≤ 32767;% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ band(i, j) = band(j, i);