(* TODO put in assert_diffs ? *)
(** We don't have ratio so we express that AG=2/3 AA' using midpoints. *)

Lemma is_gravity_center_cases : forall A B C G,
is_gravity_center G A B C \/
is_gravity_center G A C B \/
is_gravity_center G B A C \/
is_gravity_center G B C A \/
is_gravity_center G C A B \/
is_gravity_center G C B A ->
is_gravity_center G A B C.