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+Require Import Setoid.
+
+Variable A : Set.
+
+Inductive liste : Set :=
+| vide : liste
+| c : A -> liste -> liste.
+
+Inductive e : A -> liste -> Prop :=
+| ec : forall (x : A) (l : liste), e x (c x l)
+| ee : forall (x y : A) (l : liste), e x l -> e x (c y l).
+
+Definition same := fun (l m : liste) => forall (x : A), e x l <-> e x m.
+
+Definition same_refl (x:liste) : (same x x).
+ unfold same; split; intros; trivial.
+Qed.
+
+Goal forall (x:liste), (same x x).
+ intro.
+ apply (same_refl x).
+Qed.