Require Export E2_Ordre.
Section CONGRUENCE.
(* C1 : Given a line segment AB, and given a ray r originated at a point C, there exists a unique point D on the ray r such that AB = CD. *)

(* Specifications: *)
Lemma C1a : forall A B C D : Point,
A <> B ->
C <> D ->
exists E : Point, HalfLine C D E /\ Distance A B = Distance C E.
Lemma C1b : forall A B C D E F : Point,
A <> B ->
C <> D ->
HalfLine C D E ->
Distance A B = Distance C E ->
HalfLine C D F ->
Distance A B = Distance C F ->
E = F.