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+Require Export Relation_Definitions.
+Require Export Setoid.
+
+Variable A : Type.
+Variable S : A -> Type.
+Variable Seq : forall {a:A}, relation (S a).
+
+Hypothesis Seq_refl : forall {a:A} (x : S a), Seq x x.
+Hypothesis Seq_sym : forall {a:A} (x y : S a), Seq x y -> Seq y x.
+Hypothesis Seq_trans : forall {a:A} (x y z : S a), Seq x y -> Seq y z ->
+Seq x z.
+
+Add Parametric Relation a : (S a) Seq
+ reflexivity proved by Seq_refl
+ symmetry proved by Seq_sym
+ transitivity proved by Seq_trans
+ as S_Setoid.
+
+Goal forall (a : A) (x y : S a), Seq x y -> Seq x y.
+  intros a x y H.
+  setoid_replace x with y. 
+  reflexivity.
+  trivial.
+Qed.