Section Generated_module_def.
Variable R : RING.
Variable Mod : MODULE R.
Variable A : part_set Mod.
Definition generated_module : submodule Mod := coKer (FMd_lift (inj_part A)).
End Generated_module_def.

Lemma generated_module_minimal :
forall (R : RING) (Mod : MODULE R) (A : part_set Mod) (H : submodule Mod),
included A H -> included (generated_module A) H.