fact: Definition GE_J E := Zo (((E\times E) \times E)\times (E\times (E\times E))) (fun x => [/\ P (P (P x)) = P (Q x), Q (P (P x)) = P (Q (Q x)) & Q (P x) = Q (Q (Q x))]).
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)