Require Export B2_Orient_Prop.
Section COLLINEAR_PROPERTIES.

(* Specifications: *)
Lemma CollinearAAB : forall A B, Collinear A A B.
Lemma CollinearABA : forall A B, Collinear A B A.
Lemma CollinearABB : forall A B, Collinear A B B.
Lemma NotCollinearDistinctAB : forall A B C : Point,
~Collinear A B C ->
A <> B.
Lemma NotCollinearDistinctCA : forall A B C : Point,
~Collinear A B C ->
C <> A.
Lemma NotCollinearDistinctBC : forall A B C : Point,
~Collinear A B C ->
B <> C.
Lemma CollinearBCA : forall A B C,
Collinear A B C -> Collinear B C A.
Lemma CollinearCAB : forall A B C,
Collinear A B C -> Collinear C A B.
Lemma CollinearBAC : forall A B C,
Collinear A B C -> Collinear B A C.
Lemma CollinearACB : forall A B C,
Collinear A B C -> Collinear A C B.
Lemma CollinearCBA : forall A B C,
Collinear A B C -> Collinear C B A.
Lemma CollinearNotClockwiseABC : forall A B C,
Collinear A B C -> ~Clockwise A B C.
Lemma CollinearNotClockwiseBAC : forall A B C,
Collinear A B C -> ~Clockwise B A C.
Lemma ClockwiseNotCollinear : forall A B C,
Clockwise A B C ->
~Collinear A B C.
Lemma CollinearClockwiseDistinct : forall A B C D,
Collinear A B C ->
Clockwise A B D ->
C <> D.