Definition bool_groupMixin := FinGroup.Mixin addbA addFb addbb.Canonical bool_baseGroup := Eval hnf in BaseFinGroupType bool bool_groupMixin.Canonical boolGroup := Eval hnf in FinGroupType addbb.Implicit Types (s : {perm T}) (x y z : T).(** Definitions of the alternate groups and some Properties **)
Definition Sym of phant T : {set {perm T}} := setT.Local Notation "'Alt_T" := (Alt (Phant T)) (at level 0).Notation "''Alt_' T" := (Alt (Phant T))
  (at level 8, T at level 2, format "''Alt_' T") : group_scope.Notation "''Alt_' T" := (Alt_group (Phant T)) : Group_scope.

Lemma rfdP p : injective (rfd_fun p).