(* (c) Copyright 2006-2016 Microsoft Corporation and Inria.                  *)
(* Distributed under the terms of CeCILL-B.                                  *)
(*   Application of the Burside formula to count the number of distinct       *)
(* colorings of the vertices of a square and a cube.                          *)
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.

Lemma burnside_formula : forall (gT : finGroupType) s (G : {group gT}),
uniq s -> s =i G ->
forall (sT : finType) (to : {action gT &-> sT}),
(#|orbit to G @: setT| * size s)%N = \sum_(p <- s) #|'Fix_to[p]|.