
theorem
  for n be Element of NAT for x,y being FinSequence holds
  InnerVertices ((n+1)-BitAdderStr(x,y)) =
  InnerVertices (n-BitAdderStr(x,y)) \/
  InnerVertices BitAdderWithOverflowStr(x .(n+1), y.(n+1),
  n-BitMajorityOutput(x,y))
proof
  let n be Element of NAT;
  let x,y be FinSequence;
  (n+1)-BitAdderStr(x,y) = n-BitAdderStr(x,y) +*
  BitAdderWithOverflowStr(x .(n+1), y.(n+1),
  n-BitMajorityOutput(x, y)) by Th12;
  hence thesis by FACIRC_1:27;
end;
