Record Setoid : Type := 
  {Carrier :> Type; Equal : relation Carrier; Prf_equiv :> equivalence Equal}.Record Setoid : Type := 
  {Carrier :> Type; Equal : relation Carrier; Prf_equiv :> equivalence Equal}.Record Setoid : Type := 
  {Carrier :> Type; Equal : relation Carrier; Prf_equiv :> equivalence Equal}.Record Setoid : Type := 
  {Carrier :> Type; Equal : relation Carrier; Prf_equiv :> equivalence Equal}.

Lemma Refl : forall (E : Setoid) (x : E), Equal x x.