Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma proposition_31short :
forall A B C D,
BetS B D C -> nCol B C A ->
exists X Y Z, BetS X A Y /\ CongA X A D A D C /\ Par X Y B C /\ BetS X Z C /\ BetS A Z D.