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Proof step 49 from proof bxor-def-logic (previous step)

bitsand(bitsinvert(int2bits(j)), int2bits(i)) ≠ [] ∧ sgn(bitsand(bitsinvert(int2bits(i)), int2bits(j))) ≠ [] ⊦ bitsand(bitsinvert(int2bits(j)), int2bits(i)) = [], bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j)) = [], bits2int(bitsxor(int2bits(i), int2bits(j))) = bits2int(bitsor(sgn(bitsand(bitsinvert(int2bits(i)), int2bits(j))), bitsand(bitsinvert(int2bits(j)), int2bits(i)))), bitsand(bitsinvert(int2bits(i)), int2bits(j)) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ sgn(bits) = [] ↔ bits = [];