End METRIC_BASICS.
Section METRIC_PROPERTIES.

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).