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

b2i(by1) ∈byte ∧ bcompl(b2i(by2)) ∈byte ⊦ bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))) = b2i(i2b(bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))))), band(b2i(by1), bcompl(b2i(by2))) = band(b2i(by1), bcompl(b2i(by2))) ∧ b2i(i2b(band(bcompl(b2i(by1)), b2i(by2)))) = band(bcompl(b2i(by1)), b2i(by2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
~128 ≤ bcompl(b2i(by2)), bcompl(b2i(by2)) ≤ 127 ⊦ bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))) = b2i(i2b(bor(band(b2i(by1), bcompl(b2i(by2))), band(bcompl(b2i(by1)), b2i(by2))))), b2i(i2b(band(bcompl(b2i(by1)), b2i(by2)))) = band(bcompl(b2i(by1)), b2i(by2))

Rule argument

Additional information

Used simplifier rules: byte2int-in: ⊦ b2i(by) ∈byte;%inbyte: ⊦ i ∈byte ↔ ~128 ≤ i ∧ i ≤ 127;% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ band(i, j) = band(j, i);