Ltac intersection_medians G A B C I J H1 H2 H3 :=
 let T := fresh in assert(T:= intersection_two_medians_exist A B C I J H1 H2 H3);
 ex_and T G.

Lemma is_gravity_center_col : forall A B C G I, is_gravity_center G A B C -> Midpoint I A B -> Col G I C.