End T4_2.
Hint Resolve not_col_permutation_1 not_col_permutation_2
not_col_permutation_3 not_col_permutation_4 not_col_permutation_5 : col.
Section T4_3.
Context `{Tn:Tarski_neutral_dimensionless}.

(* Specifications: *)
(** This lemma is used by tactics for trying several permutations. *)
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.
End T4_3.