Ltac Col := auto 3 with col.Ltac Col5 := auto with col.

(* Specifications: *)
Lemma not_col_permutation_1 : forall (A B C : Tpoint), ~ Col A B C -> ~ Col B C A.
Lemma not_col_permutation_2 : forall (A B C : Tpoint), ~ Col A B C -> ~ Col C A B.
Lemma not_col_permutation_3 : forall (A B C : Tpoint), ~ Col A B C -> ~ Col C B A.
Lemma not_col_permutation_4 : forall (A B C : Tpoint), ~ Col A B C -> ~ Col B A C.
Lemma not_col_permutation_5 : forall (A B C : Tpoint), ~ Col A B C -> ~ Col A C B.
Lemma Col_cases : forall A B C, Col A B C \/ Col A C B \/ Col B A C \/ Col B C A \/ Col C A B \/ Col C B A -> Col A B C.
Lemma Col_perm : forall A B C, Col A B C -> Col A B C /\ Col A C B /\ Col B A C /\ Col B C A /\ Col C A B /\ Col C B A.
Lemma col_trivial_1 : forall A B, Col A A B.
Lemma col_trivial_2 : forall A B, Col A B B.
Lemma col_trivial_3 : forall A B, Col A B A.
Lemma l4_13 : forall A B C A' B' C', Col A B C -> Cong_3 A B C A' B' C' -> Col A' B' C'.
Lemma l4_14 : forall A B C A' B', Col A B C -> Cong A B A' B' -> exists C', Cong_3 A B C A' B' C'.
Lemma l4_16 : forall A B C D A' B' C' D', FSC A B C D A' B' C' D' -> A<>B -> Cong C D C' D'.
Lemma l4_17 : forall A B C P Q, A<>B -> Col A B C -> Cong A P A Q -> Cong B P B Q -> Cong C P C Q.
Lemma l4_18 : forall A B C C', A<>B -> Col A B C -> Cong A C A C' -> Cong B C B C' -> C=C'.
Lemma l4_19 : forall A B C C', Bet A C B -> Cong A C A C' -> Cong B C B C' -> C=C'.
Lemma not_col_distincts : forall A B C , ~ Col A B C -> ~ Col A B C /\ A <> B /\ B <> C /\ A <> C.
Lemma NCol_cases : forall A B C, ~ Col A B C \/ ~ Col A C B \/ ~ Col B A C \/ ~ Col B C A \/ ~ Col C A B \/ ~ Col C B A -> ~ Col A B C.
Lemma NCol_perm : forall A B C, ~ Col A B C -> ~ Col A B C /\ ~ Col A C B /\ ~ Col B A C /\ ~ Col B C A /\ ~ Col C A B /\ ~ Col C B A.
Lemma col_cong_3_cong_3_eq : forall A B C A' B' C1 C2, A <>B -> Col A B C -> Cong_3 A B C A' B' C1 -> Cong_3 A B C A' B' C2 -> C1 = C2.