Definition FMd_set := Build_Setoid eqFMd_Equiv.Definition FreeModule : MODULE R.Fixpoint FMd_lift_fun (p : FreeModule) : Mod :=
  match p with
  | Var v => f v
  | Law p1 p2 => sgroup_law Mod (FMd_lift_fun p1) (FMd_lift_fun p2)
  | Unit => monoid_unit Mod
  | Inv p1 => group_inverse Mod (FMd_lift_fun p1)
  | Op a p1 => module_mult a (FMd_lift_fun p1)
  end.Definition FMd_lift : Hom FreeModule Mod.Definition FMd_var : Hom V FreeModule.

Lemma FMd_comp_prop : Equal f (comp_hom (FMd_lift:Hom (FreeModule:SET) Mod) FMd_var).