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 ClockwiseExists : forall A B : Point, A <> B -> {C : Point | 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.