(** The six following lemmas constitute Theorem 22.5 *)

(* Specifications: *)
Lemma cong_lam__per : forall A B C D,
Lambert A B C D ->
Cong A D B C ->
Per B C D.
Lemma lam_lt__acute : forall A B C D,
Lambert A B C D ->
Lt A D B C ->
Acute B C D.
Lemma lam_lt__obtuse : forall A B C D,
Lambert A B C D ->
Lt B C A D ->
Obtuse B C D.
Lemma lam_per__cong : forall A B C D,
Lambert A B C D ->
Per B C D ->
Cong A D B C.
Lemma acute_lam__lt : forall A B C D,
Lambert A B C D ->
Acute B C D ->
Lt A D B C.
Lemma lam_obtuse__lt : forall A B C D,
Lambert A B C D ->
Obtuse B C D ->
Lt B C A D.