Definition ASpi := Angle Uu Oo Ww.

(* Specifications: *)
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.