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.