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

Lemma is_gravity_center_third_reci :
forall A B C G A' A'',
Midpoint A' B C ->
Midpoint A'' A G ->
Midpoint G A' A'' ->
~ Col A B C ->
is_gravity_center G A B C.