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

Lemma characterization_of_midpoint_F : forall A B I,
Midpoint I 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
let (Ic, _) := coordinates_of_point_F I in
let (Ix, Iy) := Ic in
Ix * 2 - (Ax + Bx) =F= 0 /\ Iy * 2 - (Ay + By) =F= 0.