diff --git a/theories/co_pset.v b/theories/co_pset.v
index 7516f56cda8f9971b0d052a15e15bf267ff20c56..3b49cb373059d3d8b1c1dda5aee2b73e14af5587 100644
--- a/theories/co_pset.v
+++ b/theories/co_pset.v
@@ -331,12 +331,11 @@ Proof.
       rewrite ?coPset_elem_of_node; naive_solver.
   * by intros [q' ->]; induction q; simpl; rewrite ?coPset_elem_of_node.
 Qed.
-
 Lemma coPset_suffixes_infinite p : ¬set_finite (coPset_suffixes p).
 Proof.
   rewrite coPset_finite_spec; simpl.
-  (* FIXME no time to finish right now, but I think it holds *)
-Abort. 
+  induction p; simpl; rewrite ?coPset_finite_node, ?andb_True; naive_solver.
+Qed.
 
 (** * Splitting of infinite sets *)
 Fixpoint coPset_l_raw (t : coPset_raw) : coPset_raw :=