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

Lemma characterization_of_equality_F : 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.