Binding constraints at second-best optimum I am dealing with ex-ante asymmetric information problems, i.e. adverse selection and in particular I cannot understand what's the intuition behind the fact that only two out of four constraints imposed in the second-best maximization problem are binding. 

To be precise, when there is asymmetric information with two types of agents, the optimum is found maximizing the utility under two individual rationality (or participation) constraints and two incentive compatibility constraints. In order to simplify the computations, it can be proven that the IC for the high type agent and the IR for the low type agent are binding, whereas the other two constraints are redundant. 

I have seen the proof and it is pretty clear but what I cannot understand is the economic intuition behind the proof; Is there someone that has this kind  of intuition?
I think its not a complex issue: 

a) You need to keep the high type agent from pretending to be the ow type agent, so you give him an extra compensation from showing his high type. But this nice deal pays him more than necessary to keep him in the game so his IR is more than satisfied, i.e. not binding. 

b) Similarly, you will make it painful to show that you are a low type, so that the high type doesn't go there, but you can;t make it so painful that the low type doesn't want to play so you pay him the minimum amount that he will take, i.e. his IR is binding, but  he would never choose to show himself as the high type anyway because with his low type, the incentives don't work in his favor, so the IC is not binding.