(* 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. *)

(* Specifications: *)
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.
Lemma C4b : forall A B C D F : Point,
A <> B ->
A <> C ->
D <> F ->
exists E : Point,
D <> E /\
~Clockwise D E F /\
Angle B A C = Angle  E D F.
Lemma C4c : forall A B C D F E E' : Point,
A <> B ->
A <> C ->
D <> F ->
D <> E ->
D <> E' ->
~Clockwise D E F ->
~Clockwise D E' F ->
Angle B A C = Angle  E D F ->
Angle B A C = Angle  E' D F ->
Superimposed (HalfLine D E) (HalfLine D E').
Lemma C4d : forall A B C D F E E' : Point,
A <> B ->
A <> C ->
D <> F ->
D <> E ->
D <> E' ->
~Clockwise D F E ->
~Clockwise D F E' ->
(Angle B A C) = (Angle  E D F) ->
(Angle B A C) = (Angle  E' D F) ->
Superimposed (HalfLine D E) (HalfLine D E').