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 Archimedian : forall A B C : Point,
A <> B -> exists n : nat, LSlt (Distance A C) (DistTimesn n A B).