proposition: Lemma generated_module_prop_rev : forall (R : RING) (Mod : MODULE R) (A : part_set Mod) (y : Mod), (exists x : FMd R A, Equal y (FMd_lift (inj_part A) x)) -> in_part y (generated_module A).
proof: Proof. intros R Mod 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: Module_kernel Free_module