Require Export B4_Droite_Def.
Section BETWEEN_PRELIMINARS.

(* Specifications: *)
Lemma BetweenDistinctAB : forall A B C, Between A B C -> A <> B.
Lemma BetweenNotClockwiseABC : forall A B C,
Between A B C -> ~Clockwise A B C.
Lemma ClockwiseNotBetweenABC : forall A B C,
Clockwise A B C -> ~Between A B C.
Lemma BetweenNotClockwiseBAC : forall A B C,
Between A B C -> ~Clockwise B A C.
Lemma BetweenHalfLine : forall A B C,
Between A B C -> HalfLine A B C.
Lemma BetweenSymHalfLine : forall A B C,
Between A B C -> HalfLine C B A.