proposition: Lemma generated_module_prop : forall (R : RING) (Mod : MODULE R) (A : part_set Mod) (y : Mod), in_part y (generated_module A) -> exists x : FMd R A, Equal y (FMd_lift (inj_part A) x).
proof: Proof. simpl in |- *; auto with algebra. intros R Mod 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: Module_kernel Free_module