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_cases : forall A B C G, is_gravity_center G A B C \/ is_gravity_center G A C B \/ is_gravity_center G B A C \/ is_gravity_center G B C A \/ is_gravity_center G C A B \/ is_gravity_center G C B A -> is_gravity_center G A B C.