Definition CongruentTriangles (A B C A' B' C' : Point) :=
	Distance A B = Distance A' B' /\
	Distance B C = Distance  B' C' /\
	Distance C A = Distance C' A'.

(* Specifications: *)
Lemma CongruentTrianglesSym : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> CongruentTriangles A' B' C' A B C.
Lemma CongruentTrianglesBAC : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> CongruentTriangles B A C B' A' C'.
Lemma CongruentTrianglesACB : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> CongruentTriangles A C B A' C' B'.
Lemma CongruentTrianglesCBA : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> CongruentTriangles C B A C' B' A'.
Lemma CongruentTrianglesBCA : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> CongruentTriangles B C A B' C' A'.
Lemma CongruentTrianglesCAB : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> CongruentTriangles C A B C' A' B'.
Lemma CongruentTrianglesAB : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> Distance A B = Distance A' B'.
Lemma CongruentTrianglesBC : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> Distance B C = Distance B' C'.
Lemma CongruentTrianglesCA : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> Distance C A = Distance C' A'.
Lemma CongruentTrianglesA : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> A <> B -> A <> C -> Angle B A C = Angle B' A' C'.
Lemma CongruentTrianglesB : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> B <> A -> B <> C -> Angle A B C = Angle A' B' C'.
Lemma CongruentTrianglesC : forall A B C A' B' C' : Point, CongruentTriangles A B C A' B' C' -> C <> A -> C <> B -> Angle A C B = Angle A' C' B'.
Lemma CongruentTrianglesSASA : 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' -> A <> B -> A <> C -> CongruentTriangles A B C A' B' C'.
Lemma CongruentTrianglesSASB : 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' -> B <> A -> B <> C -> CongruentTriangles A B C A' B' C'.
Lemma CongruentTrianglesSASC : 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' -> C <> A -> C <> B -> CongruentTriangles A B C A' B' C'.