Definition generated_module : submodule Mod := coKer (FMd_lift (inj_part A)).

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).