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+(* Check some aspects of that the algorithm used to possibly reuse a
+   global name in the recursive calls (coinductive case) *)
+
+CoInductive Str : Set := Cons (h:nat) (t:Str).
+
+Definition decomp_func (s:Str) :=
+  match s with
+    | Cons h t => Cons h t
+  end.
+
+Theorem decomp s: s = decomp_func s.
+Proof.
+  intros s.
+  case s; simpl; reflexivity.
+Qed.
+
+Definition zeros := (cofix z : Str := Cons 0 z).
+Lemma zeros_rw : zeros = Cons 0 zeros.
+  rewrite (decomp zeros).
+  simpl.
+Admitted.