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 sc1 sc2,
forall s, clause_denote sc2 s ->
listd clause_denote inter TT (unfolding2 sc1 sc2) s.