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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fqup.ma
index d0be90869..cc74f1cef 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpr_fqup.ma
@@ -20,9 +20,23 @@ include "basic_2/rt_transition/lfpr.ma".
 (* Advanced properties ******************************************************)
 
 (* Note: lemma 250 *)
+(* Basic_2A1: uses: lpr_refl *)
 lemma lfpr_refl: ∀h,G,T. reflexive … (lfpr h G T).
 /2 width=1 by lfxs_refl/ qed.
 
-lemma lfpr_pair: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 →
-                 ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ➡[h, T] L.ⓑ{I}V2.
-/2 width=1 by lfxs_pair/ qed.
+(* Basic_2A1: uses: lpr_pair *)
+lemma lfpr_pair_refl: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 →
+                      ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ➡[h, T] L.ⓑ{I}V2.
+/2 width=1 by lfxs_pair_refl/ qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma lfpr_inv_bind_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 →
+                          ∧∧ ⦃G, L1⦄ ⊢ ➡[h, V] L2 & ⦃G, L1.ⓧ⦄ ⊢ ➡[h, T] L2.ⓧ.
+/2 width=3 by lfxs_inv_bind_void/ qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma lfpr_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T.
+                             ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 → ⦃G, L1.ⓧ⦄ ⊢ ➡[h, T] L2.ⓧ.
+/2 width=4 by lfxs_fwd_bind_dx_void/ qed-.