If "L" is a regular language, then by definition there is a DFA "A" that recognizes it, with only finitely many states. If there are "n" states, then partition the set of all finite strings into "n" subsets, where subset "Si" is the set of strings that, when given as input to automaton "A", cause it to end in state "i". For every two strings "x" and "y" that belong to the same subset, and for every choice of a third string "z", automaton "A" reaches the same state on input "xz" as it reaches on input "yz", and therefore must either accept both of the inputs "xz" and "yz" or reject both of them. Therefore, no string "z" can be a distinguishing extension for "x" and "y", so they must be related by "RL". Thus, "Si" is a subset of an equivalence class of "RL". Combining this fact with the fact that every member of one of these equivalence classes belongs to one of the sets "Si", this gives a many-to-one relation from states of "A" to equivalence classes, implying that the number of equivalence classes is finite and at most "n".