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.

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).