  A proof procedure, in the spirit of the sequent calculus, is proposed to
check the validity of entailments between Separation Logic formulas combining
inductively defined predicates denoted structures of bounded tree width and
theory reasoning. The calculus is sound and complete, in the sense that a
sequent is valid iff it admits a (possibly infinite) proof tree. We show that
the procedure terminates in the two following cases: (i) When the inductive
rules that define the predicates occurring on the left-hand side of the
entailment terminate, in which case the proof tree is always finite. (ii) When
the theory is empty, in which case every valid sequent admits a rational proof
tree, where the total number of pairwise distinct sequents occurring in the
proof tree is doubly exponential w.r.t.\ the size of the end-sequent.
