Definition Inter := fun X P Q R S =>
  P<>Q /\ R <> S /\ Col X P Q /\ Col X R S /\ 
  ((exists X, Col X P Q /\ ~ Col X R S) \/ (exists X, ~ Col X P Q /\ Col X R S)).

(* Specifications: *)
Lemma col_transitivity_1 : forall P Q A B, P<>Q -> Col P Q A -> Col P Q B -> Col P A B.
Lemma col_transitivity_2 : forall P Q A B, P<>Q -> Col P Q A -> Col P Q B -> Col Q A B.
Theorem l6_21 : forall A B C D P Q, ~ Col A B C -> C<>D -> Col A B P -> Col A B Q -> Col C D P -> Col C D Q -> P=Q.
Lemma l6_25 : forall A B, A<>B -> exists C, ~ Col A B C.
Theorem t2_8 : forall A B C D E : Point, Bet A B C -> Bet D B E -> Cong A B D B -> Cong B C B E -> Cong A E C D.