Definition Rule_U3 (nc pc : clause) :=
 match nc , pc with
   PosSpaceClause Gamma Delta ((Lseg x y)::Sigma) ,
   NegSpaceClause Gamma' (Lseg x' Nil::Sigma') Delta' =>
     match expr_cmp x x' with
      Eq => Some (NegSpaceClause Gamma' (Lseg x y::Lseg y Nil::Sigma') Delta')
     |_ => None
     end
  | _ , _ => None
 end.

Lemma U5_axiom: forall x y z w sigma' sigma h (K: (sepcon (lseg x y) (sepcon (lseg z w) sigma')) h) (K': (sepcon (lseg x y) (sepcon (lseg y z) sigma)) h), (z=w \/ (sepcon (lseg x z) sigma) h).