Lemma proposition_45 : forall A B C D E J K N O R S, nCol J E N -> nCol A B D -> nCol C B D -> BetS A O C -> BetS B O D -> neq R K -> nCol K R S -> exists X Z U, PG X K Z U /\ CongA X K Z J E N /\ EF X K Z U A B C D /\ Out K R Z /\ OS X S K Z.