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. *)
(* C2 : If AB = CD and AB = EF, then CD = EF. Every line segment is congruent to itself. *)
(* C3 : Given three points A, B, C on a line satisfying A - B - C, and three further points D, E, F on a line satisfying D - E - F, if AB = DE and BC = EF, then AC = DF. *)

Lemma C3 : forall A B C D E F : Point,
Between A B C ->
Between D E F ->
Distance A B = Distance D E ->
Distance B C = Distance E F ->
Distance A C = Distance D F.