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Proof step 43 from proof bxor-def-logic (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
bitsand(bitsinvert(int2bits(i)), int2bits(j)) = [] ⊦ bitsand(sgn(bitsinvert(int2bits(i))), int2bits(j)) = [], bits2int(bitsxor(int2bits(i), int2bits(j))) = bits2int(bitsor(sgn(bitsand(bitsinvert(int2bits(j)), int2bits(i))), []))

Rule argument

Additional information

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