proposition: Lemma generated_group_prop_rev : forall (G : GROUP) (A : part_set G) (y : G), (exists x : FG A, Equal y (FG_lift (inj_part A) x)) -> in_part y (generated_group A).
proof: Proof. intros G A y H'; try assumption. elim H'; intros x E; try exact E; clear H'. simpl in |- *; auto with algebra. exists x; split; [ idtac | try assumption ]. auto with algebra. Qed.
imports: Group_kernel Free_group