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 three_medians_intersect: forall A B C I J K, ~Col A B C -> Midpoint I B C -> Midpoint J A C -> Midpoint K A B -> exists G, Col G A I /\ Col G B J /\Col G C K.