Instance lt_strorder : StrictOrder lt.
Definition compare t1 t2 :=
let ft1 := fstpp(t1) in
let ft2 := fstpp(t2) in
let st1 := sndpp(t1) in
let st2 := sndpp(t2) in
match (Pos.compare ft1 ft2) with
| Lt => Lt
| Eq => Pos.compare st1 st2
| Gt => Gt
end.

Lemma compare_spec : forall t1 t2, CompSpec eq lt t1 t2 (compare t1 t2).
End SetOfPairsOfPositiveOrderedType.