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. *)
(* C4 : Given an angle ^BAC and given a ray DF, there exists a unique ray DE on a given side of the line DF, such that ^BAC = ^EDF. *)

Lemma C4a : forall A B C D F : Point,
A <> B ->
A <> C ->
D <> F ->
exists E : Point,
D <> E /\
~Clockwise D F E /\
Angle B A C = Angle  E D F.