Section METRIC.
Parameter  Distance : Point -> Point -> LS.
Definition Equidistant := fun A B C D =>
Distance A B = Distance C D.
Fixpoint DistTimesn (n : nat) (A B : Point) {struct n}: LS :=
match n with
| O => Distance A A
| S p => LSplus (Distance A B) (DistTimesn p A B)
end.

Axiom LSltOrder : forall A B C,
HalfLine A B C \/ HalfLine A C B ->
LSlt (Distance A B) (Distance A C) ->
(EquiOriented A B B C) /\ (B <> C).