(** * Proposition 4 If in a circle two straight lines cut one another which are not through the center, they do not bisect one another. *)

Lemma prop_4 : forall O P A B C D X, B <> C -> A <> B ->
OnCircle A O P ->
OnCircle B O P ->
OnCircle C O P ->
OnCircle D O P ->
Midpoint X A C ->
Midpoint X B D ->
X = O.