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_perm : forall A B C G, is_gravity_center G A B C -> 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.