Definition is_gravity_center G A B C :=
 ~ Col A B C /\
 exists I, exists J, Midpoint I B C /\ Midpoint J A C /\ Col G A I /\ Col G B J.

(* Specifications: *)
Lemma is_gravity_center_coplanar : forall A B C G, is_gravity_center G A B C -> Coplanar G A B C.
Lemma is_gravity_center_exist_unique : forall A B C, ~ Col A B C -> exists! G, is_gravity_center G A B C.