Lemma impossible_two_sides_not_col : forall A B C D T Y, A <> B -> A <> C -> A <> D -> A <> T -> A <> Y -> B <> C -> B <> D -> B <> T -> B <> Y -> C <> D -> C <> T -> C <> Y -> D <> T -> T <> Y -> ~ Col A B C -> Bet A D T -> ~ Col B C T -> Bet B D C -> Bet B Y T -> ~ Col A C Y.