Definition LS0 := Distance Oo Oo.

Lemma ChaslesAssoc : forall A B C D : Point, HalfLine A B C -> HalfLine C B A -> HalfLine A B D -> HalfLine D B A -> HalfLine B C D -> HalfLine D C B -> HalfLine A C D -> HalfLine D C A -> LSplus (Distance A B) (LSplus (Distance B C) (Distance C D)) = LSplus (LSplus (Distance A B) (Distance B C)) (Distance C D).