Definition lt (t1 t2 : t) :=
    let ft1 := fstpp(t1) in
    let ft2 := fstpp(t2) in
    let st1 := sndpp(t1) in
    let st2 := sndpp(t2) in
    if Pos.eqb ft1 ft2 then Pos.lt st1 st2
                       else Pos.lt ft1 ft2.

Lemma lt_trans : Transitive lt.