Module OrderedPair (X:OrderedType) (Y:OrderedType) <: OrderedType with
Definition t := (X.t * Y.t)%type.
Definition t := (X.t * Y.t)%type.
Definition eq (xy1:t) (xy2:t) :=
let (x1,y1) := xy1 in
let (x2,y2) := xy2 in
(X.eq x1 x2) /\ (Y.eq y1 y2).
Definition lt (xy1:t) (xy2:t) :=
let (x1,y1) := xy1 in
let (x2,y2) := xy2 in
(X.lt x1 x2) \/ ((X.eq x1 x2) /\ (Y.lt y1 y2)).

Lemma eq_refl : forall (x:t),(eq x x).