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 unfolding6NPR'_sound: forall sigma2 sigma0 sigma1 sig2' p s, In (p,sig2') (unfolding6NPR' sigma0 sigma1 sigma2) -> space_denote sigma1 s -> space_denote sig2' s -> pure_atom_denote p s \/ (space_denote (sigma0++ sigma2)) s.