simpl in |- *.
intros x H';
exists (Var R (V:=A) (Build_subtype (E:=R) (P:=A) (subtype_elt:=x) H'));
split; [ idtac | try assumption ].
auto with algebra.
simpl in |- *.
auto with algebra.
Qed.

Lemma generated_ideal_minimal :
forall I : ideal R, included A I -> included generated_ideal I.