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 U7_axiomSchema: forall x y z u Sigma s, space_denote (Lseg y z::Lseg z y::Lseg x y::Lseg u z::Sigma) s -> space_denote (Lseg x z::Lseg u y::Sigma) s.