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_antiref : forall x, ~ lt x x.