Definition CongruentStrictTriangles (A B C A' B' C' : Point) :=
	CongruentTriangles A B C A' B' C' /\
	~Collinear A B C.

(* Specifications: *)
Lemma CongruentStrictTrianglesSym : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> CongruentStrictTriangles A' B' C' A B C.
Lemma CongruentStrictTrianglesBAC : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> CongruentStrictTriangles B A C B' A' C'.
Lemma CongruentStrictTrianglesACB : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> CongruentStrictTriangles A C B A' C' B'.
Lemma CongruentStrictTrianglesCBA : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> CongruentStrictTriangles C B A C' B' A'.
Lemma CongruentStrictTrianglesBCA : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> CongruentStrictTriangles B C A B' C' A'.
Lemma CongruentStrictTrianglesCAB : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> CongruentStrictTriangles C A B C' A' B'.
Lemma CongruentStrictTrianglesAB : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> Distance A B = Distance A' B'.
Lemma CongruentStrictTrianglesBC : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> Distance B C = Distance B' C'.
Lemma CongruentStrictTrianglesCA : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> Distance C A = Distance C' A'.
Lemma CongruentStrictTrianglesA : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> Angle B A C = Angle B' A' C'.
Lemma CongruentStrictTrianglesB : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> Angle A B C = Angle A' B' C'.
Lemma CongruentStrictTrianglesC : forall A B C A' B' C' : Point, CongruentStrictTriangles A B C A' B' C' -> Angle A C B = Angle A' C' B'.
Lemma CongruentStrictTrianglesSASA : forall A B C A' B' C' : Point, Distance A B = Distance A' B' -> Distance A C = Distance A' C' -> Angle B A C = Angle B' A' C' -> ~Collinear A B C -> CongruentStrictTriangles A B C A' B' C'.
Lemma CongruentStrictTrianglesSASB : forall A B C A' B' C' : Point, Distance B A = Distance B' A' -> Distance B C = Distance B' C' -> Angle A B C = Angle A' B' C' -> ~Collinear A B C -> CongruentStrictTriangles A B C A' B' C'.
Lemma CongruentStrictTrianglesSASC : forall A B C A' B' C' : Point, Distance C A = Distance C' A' -> Distance C B = Distance C' B' -> Angle A C B = Angle A' C' B' -> ~Collinear A B C -> CongruentStrictTriangles A B C A' B' C'.
Lemma EquiDirectedCollinear : forall A B C : Point, EquiDirected A B B C -> Collinear A B C.
Lemma ClockwiseEq : forall A B C D : Point, Clockwise A B C -> Collinear A B D -> Collinear B C D -> B = D.
Lemma CongruentStrictTrianglesASAAB : forall A B C A' B' C' : Point, Distance A B = Distance A' B' -> Angle B A C = Angle B' A' C' -> Angle A B C = Angle A' B' C' -> ~Collinear A B C -> CongruentStrictTriangles A B C A' B' C'.
Lemma CongruentStrictTrianglesASABC : forall A B C A' B' C' : Point, Distance B C = Distance B' C' -> Angle A B C = Angle A' B' C' -> Angle B C A = Angle B' C' A' -> ~Collinear A B C -> CongruentStrictTriangles A B C A' B' C'.
Lemma CongruentStrictTrianglesASACA : forall A B C A' B' C' : Point, Distance C A = Distance C' A' -> Angle B C A = Angle B' C' A' -> Angle B A C = Angle B' A' C' -> ~Collinear A B C -> CongruentStrictTriangles A B C A' B' C'.