Ltac Cong := auto 4 with cong.Ltac eCong := eauto with cong.

(* Specifications: *)
Lemma not_cong_2134 : forall A B C D, ~ Cong A B C D -> ~ Cong B A C D.
Lemma not_cong_1243 : forall A B C D, ~ Cong A B C D -> ~ Cong A B D C.
Lemma not_cong_2143 : forall A B C D, ~ Cong A B C D -> ~ Cong B A D C.
Lemma not_cong_3412 : forall A B C D, ~ Cong A B C D -> ~ Cong C D A B.
Lemma not_cong_4312 : forall A B C D, ~ Cong A B C D -> ~ Cong D C A B.
Lemma not_cong_3421 : forall A B C D, ~ Cong A B C D -> ~ Cong C D B A.
Lemma not_cong_4321 : forall A B C D, ~ Cong A B C D -> ~ Cong D C B A.
Lemma five_segment_with_def : forall A B C D A' B' C' D', OFSC A B C D A' B' C' D' -> A<>B -> Cong C D C' D'.
Lemma cong_diff : forall A B C D : Tpoint, A <> B -> Cong A B C D -> C <> D.
Lemma cong_diff_2 : forall A B C D , B <> A -> Cong A B C D -> C <> D.
Lemma cong_diff_3 : forall A B C D , C <> D -> Cong A B C D -> A <> B.
Lemma cong_diff_4 : forall A B C D , D <> C -> Cong A B C D -> A <> B.
Lemma cong_3_sym : forall A B C A' B' C', Cong_3 A B C A' B' C' -> Cong_3 A' B' C' A B C.
Lemma cong_3_swap : forall A B C A' B' C', Cong_3 A B C A' B' C' -> Cong_3 B A C B' A' C'.
Lemma cong_3_swap_2 : forall A B C A' B' C', Cong_3 A B C A' B' C' -> Cong_3 A C B A' C' B'.
Lemma cong3_transitivity : forall A0 B0 C0 A1 B1 C1 A2 B2 C2, Cong_3 A0 B0 C0 A1 B1 C1 -> Cong_3 A1 B1 C1 A2 B2 C2 -> Cong_3 A0 B0 C0 A2 B2 C2.
Lemma eq_dec_points : forall A B : Tpoint, A=B \/ ~ A=B.
Lemma distinct : forall P Q R : Tpoint, P <> Q -> (R <> P \/ R <> Q).
Lemma l2_11 : forall A B C A' B' C', Bet A B C -> Bet A' B' C' -> Cong A B A' B' -> Cong B C B' C' -> Cong A C A' C'.
Lemma bet_cong3 : forall A B C A' B', Bet A B C -> Cong A B A' B' -> exists C', Cong_3 A B C A' B' C'.
Lemma construction_uniqueness : forall Q A B C X Y, Q <> A -> Bet Q A X -> Cong A X B C -> Bet Q A Y -> Cong A Y B C -> X=Y.
Lemma Cong_cases : forall A B C D, Cong A B C D \/ Cong A B D C \/ Cong B A C D \/ Cong B A D C \/ Cong C D A B \/ Cong C D B A \/ Cong D C A B \/ Cong D C B A -> Cong A B C D.
Lemma Cong_perm : forall A B C D, Cong A B C D -> Cong A B C D /\ Cong A B D C /\ Cong B A C D /\ Cong B A D C /\ Cong C D A B /\ Cong C D B A /\ Cong D C A B /\ Cong D C B A.