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

Lemma characterization_of_collinearity_F : forall A B C,
Col 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
(Ax - Bx) * (By - Cy) - (Ay - By) * (Bx - Cx) =F= 0.