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.