Lemma l3_43 : forall O A B X Y C D P Q R T r, mratio C A B r -> mratio D A B (0-r) -> inter_ll P O A X Y -> inter_ll Q O B X Y -> inter_ll R O C X Y -> inter_ll T O D X Y -> parallel P R R Q -> R<>Q -> parallel T P T Q -> T<>Q -> P<>T -> P<>R -> ~ Col P X Y -> harmonic P Q R T.