Definition Qpositive2 := (Qpositive * Qpositive)%type.
Definition bin2_lt (x y : Qpositive2) :=
let (p1, p2) := x in let (p1', p2) := y in bin_lt p1 p1'.
Definition bin2_eq (x y : Qpositive2) :=
let (p1, p2) := x in let (p1', p2) := y in p1 = p1'.

Lemma bin2_eq_is_equality : is_equality Qpositive2 bin2_eq.