Definition sqrt3 := PythF 1 (PythF 1 1).

Lemma characterization_of_neq_F_bis : forall A B, A <> B <-> let (Ac, _) := coordinates_of_point_F A in let (Ax, Ay) := Ac in let (Bc, _) := coordinates_of_point_F B in let (Bx, By) := Bc in ~ (Ax =F= Bx) \/ ~ (Ay =F= By).