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_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.