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 U2_sound: forall nc pc c s,
clause_denote nc s -> clause_denote pc s ->
Rule_U2 nc pc = Some c ->
clause_denote c s.