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

Lemma characterization_of_betweenness_F : forall A B C, Bet A B C <-> 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 let (Cc, _) := coordinates_of_point_F C in let (Cx, Cy) := Cc in exists T, 0 <= T /\ T <= 1 /\ T * (Cx - Ax) =F= Bx - Ax /\ T * (Cy - Ay) =F= By - Ay.