Require Export D3_Triangle_Prop.
Section CONSEQUENCES.

(* Specifications: *)
Lemma AS0diffASpi : AS0  <> ASpi.
Lemma ElongatedAngleBetween : forall A B C : Point,
A <> B ->
A <> C ->
Angle B A C = ASpi ->
Between B A C.
Lemma ProperAngle : forall A B C : Point,
Clockwise B A C ->
Angle B A C <> AS0 /\ Angle B A C <> ASpi.
Lemma EqualAngleHalfLineB : forall A B B' C : Point,
A <> C ->
A <> B ->
A <> B' ->
~Clockwise A B C ->
~Clockwise A B' C ->
(Angle  B A C) = (Angle  B' A C) ->
HalfLine A B B'.
Lemma EqualAngleHalfLineC : forall A B C C' : Point,
A <> B ->
A <> C ->
A <> C' ->
~Clockwise A B C ->
~Clockwise A B C' ->
(Angle  C A B) = (Angle  C' A B) ->
HalfLine A C C'.