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.