Module SetOfPairsOfPositiveOrderedType <: OrderedType.
Definition t:= (positive * positive).
Definition eq (t1 t2 : t) :=
Pos.eq (fstpp(t1)) (fstpp(t2)) /\ Pos.eq (sndpp(t1)) (sndpp(t2)).
Include IsEq.
Definition eqb (t1 t2 : t) :=
Pos.eqb (fstpp(t1)) (fstpp(t2)) && Pos.eqb (sndpp(t1)) (sndpp(t2)).

Lemma eqb_eq : forall t1 t2, eqb t1 t2 = true <-> eq t1 t2.