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 U4: forall x y z w sigma l s
(SD1 : space_denote (Lseg x y :: Lseg y z :: sigma) s)
(SD2: space_denote (Lseg x y :: Next z w :: l) s),
space_denote (Lseg x z :: sigma) s.