Verify the following version of the principle of recursive definition: Let A be a set. Let...

Verify the following version of the principle of recursive definition: Let A be a set. Let ρ be a function assigning, to every function f mapping a section Sn of  into A, an element ρ(f) of A. Then there is a unique function  such that h(n) = ρ(h\Sn) for each .