Hint Immediate col_trivial_1 col_trivial_2 col_trivial_3: col.
Section T4_4.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
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.