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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
index 18e245959..7f71bea7c 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
@@ -40,3 +40,21 @@ lemma cnv_fwd_aaa (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ∃A. ⦃G, L
   /3 width=3 by aaa_cast, ex_intro/
 ]
 qed-.
+
+(* Forward lemmas with t_bound rt_transition for terms **********************)
+
+lemma cnv_fwd_cpm_SO (a) (h) (G) (L):
+      ∀T. ⦃G, L⦄ ⊢ T ![a, h] → ∃U. ⦃G,L⦄ ⊢ T ➡[1,h] U.
+#a #h #G #L #T #H
+elim (cnv_fwd_aaa … H) -H #A #HA
+/2 width=2 by aaa_cpm_SO/
+qed-.
+
+(* Forward lemmas with t_bound rt_computation for terms *********************)
+
+lemma cnv_fwd_cpms_total (a) (h) (n) (G) (L):
+      ∀T. ⦃G, L⦄ ⊢ T ![a, h] → ∃U. ⦃G,L⦄ ⊢ T ➡*[n,h] U.
+#a #h #n #G #L #T #H
+elim (cnv_fwd_aaa … H) -H #A #HA
+/2 width=2 by aaa_cpms_total/
+qed-.