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)).

Lemma col_transitivity_1 : forall P Q A B, P<>Q -> Col P Q A -> Col P Q B -> Col P A B.