Lemma l6_44 : forall A B C G P Q, is_centroid G A B C -> on_inter_line_parallel P G A B B C -> on_inter_line_parallel Q G A C B C -> G<>Q -> G<>P -> 1+2 <> 0 -> 2*2*S4 P Q C B = (2+2+1)* S A Q P.