Lemma impossible_case_1 : forall A B C D T x y, A <> B -> A <> C -> A <> D -> A <> T -> B <> C -> B <> D -> B <> T -> C <> D -> C <> T -> D <> T -> x <> y -> ~ Col A B C -> Bet A D T -> ~ Col B C T -> Bet B D C -> Bet A B x -> Bet C y A -> Bet x T y -> Par_strict B C x y -> False.