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.