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 unfolding3'_sound: forall sigma2 sigma0 sigma1 sig2' s, In sig2' (unfolding3' sigma0 sigma1 sigma2) -> space_denote sig2' s -> space_denote (sigma0++sigma2) s.