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diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_succ_iter.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_succ_iter.ma
index b3eee2068..7f47f9158 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_succ_iter.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_succ_iter.ma
@@ -17,8 +17,9 @@ include "ground/arith/nat_succ.ma".
 
 (* SUCCESSOR FOR NON-NEGATIVE INTEGERS **************************************)
 
-(* Rewrites with niter ******************************************************)
+(* Constructions with niter *************************************************)
 
-lemma niter_succ (A) (f) (n) (a): f (f^n a) = f^{A}(↑n) a.
+(*** iter_S *)
+lemma niter_succ (A) (f) (n): f ∘ f^n ≐ f^{A}(↑n).
 #A #f * //
 qed.