Newton-Puiseux Theorem for convergent generalised power series

A generalised power series (in several variables) is a series with real nonnegative exponents whose support is contained in a cartesian product of well-ordered subsets of the real line. Let A be the collection of all convergent generalised power series. I will show that, if f(x_1,…,x_n,y) is in A, then the solutions y=g(x_1,…,x_n) of the equation f=0 can be expressed as terms of the language which has a symbol for every function in A and a symbol for division. The construction of the terms is rather explicit. If instead of solving just one equation one wants to solve a system of equations, then one needs a different argument and the proof I will exhibit is a lot less constructive.