Lemma sesamath_4ieme_G2_ex45 : forall A B C I K J M G, ~ Col A B C -> Midpoint I B C -> Col I A M -> Midpoint A I M -> Midpoint J A I -> Par J K A C -> Col K I C -> Col G C A /\ Col G M K -> Midpoint K I C /\ Par A K M C /\ is_gravity_center G C M I.