End ANGLE_PROPERTIES.
Section PARTICULAR_ANGLES.
Definition AS0 := Angle Uu Oo Uu.
Definition Ww : Point.

(* Specifications: *)
Lemma DistinctOoWw : Oo <> Ww.
Lemma BetweenUuOoWw : Between Uu Oo  Ww.
Lemma BetweenWwOoUu : Between Ww Oo  Uu.
Definition ASpi := Angle Uu Oo Ww.
Lemma NullAngle : forall A B C : Point,
A <> B ->
HalfLine A B C ->
Angle B A C = AS0.
Lemma ElongatedAngle : forall A B C : Point,
Between A B C ->
Angle A B C = ASpi.
Lemma NullAngleHalfLine : forall A B C : Point,
A <> B ->
A <> C ->
Angle B A C = AS0 ->
HalfLine A B C.
Lemma ElongatedAngleChasles : forall A B C : Point,
A <> B ->
A <> C ->
Angle B A C = ASpi ->
LSplus (Distance B A) (Distance A C) = Distance B C.
Lemma ElongatedAngleRec : forall A B C : Point,
A <> B ->
A <> C ->
Angle B A C = ASpi ->
Between B A C.