An airfoil and the flow of air around it are a system that produces lift. The four theories that each describe some aspect of the system behavior are integrated by the system and can't exist independently of each other except outside the system. In other words, the downwash can't exist without the circulation, the pressure distribution and the velocity distribution. The existance of each depends on the existance of all the others. So, what sense dose it make to talk about how much of the lift is contributed by which part of the system?