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 : forall A B C G G' A', is_gravity_center G A B C -> Midpoint G' A G -> Midpoint A' B C -> Midpoint G A' G'.