Require Export B6_Cercle_Def.
Section EQUILATERAL_TRIANGLE.
Definition Equilateral (A B C : Point) :=
Distance A B = Distance A C /\
Distance A B = Distance B C.

(* Specifications: *)
Lemma DegeneratedEquilateral : forall A : Point,
Equilateral A A A.
Lemma Exists2AB : forall A B : Point,
A <> B ->
{C : Point |
Between A B C /\
Distance B C = Distance A B}.
Lemma EquilateralLSlt : forall A B : Point,
A<>B -> LSlt (Distance A B) (LSplus (Distance A B) (Distance A B)).
Lemma EquilateralSpec : forall A B : Point,
A<>B -> TriangleSpec (Distance A B) (Distance A B) (Distance A B).
Lemma EquilateralClockwise : forall A B : Point,
A <> B ->
{C : Point | Equilateral A B C /\ Clockwise A B C}.
Lemma ThirdPoint : {Vv : Point | Clockwise Oo Uu Vv}.
Lemma  Apart : forall A B C : Point,
A <> B -> A <> C \/ B <> C.