Proving Fixed Points

We propose a method to characterize the fixed points described in Tarski's theorem for complete lattices. The method is deductive: the least and greatest fixed points are "proved" in some inference system defined from deduction rules. We also apply the method to two other fixed point theorems, a generalization of Tarski's theorem to chain-complete posets and Bourbaki-Witt's theorem. Finally, we compare the method with the traditional iterative method resorting to ordinals and the original impredicative method used by Tarski