Section Dec_in_Prop.
Variables (A:Type)(dec:decidable_eq A).
Proof using A dec.
induction l as [|a l IH].
- now right.
- destruct (dec a x).
+ left. now left.
+ destruct IH; simpl; [left|right]; tauto.
Qed.

Lemma incl_decidable (l l':list A) : decidable (incl l l').