proposition: Lemma generated_group_prop : forall (G : GROUP) (A : part_set G) (y : G), in_part y (generated_group A) -> exists x : FG A, Equal y (FG_lift (inj_part A) x).
proof: Proof. simpl in |- *; auto with algebra. intros G A y H'; try assumption. elim H'; intros x E; elim E; intros H'0 H'1; try exact H'1; clear E H'. exists x; try assumption. Qed.
imports: Group_kernel Free_group