Definition Rule_U2 (nc pc : clause) :=
match nc , pc with
PosSpaceClause Gamma Delta ((Next x y)::Sigma) ,
NegSpaceClause Gamma' (Lseg x' z::Sigma') Delta' =>
match expr_cmp x x' with
Eq => Some (NegSpaceClause Gamma' (Next x y::Lseg y z::Sigma')
(Eqv x z :: Delta'))
|_ => None
end
| _ , _ => None
end.

Lemma unfolding2'_sound: forall  sigma2 sigma0 sigma1 p sig2' s,
In (p,sig2') (unfolding2' sigma0 sigma1 sigma2) ->
space_denote sig2' s ->
(pure_atom_denote p s \/ space_denote (sigma0++sigma2) s).