Lemma l6_15 : forall A B O C D r, is_midpoint O A B -> on_line_d C O A r -> on_line_d D O A (1/r) -> r <> 0 -> parallel A C C B -> parallel D A D B -> C<>B -> D<>B -> A<>D -> A<>C -> r+1 <> 0 -> harmonic A B C D.