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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
index 76ff1a2a1..a77772154 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_sub.ma
@@ -21,39 +21,39 @@ include "basic_2/dynamic/cnv.ma".
 (* Inductive premises for the preservation results **************************)
 
 definition IH_cnv_cpm_trans_lpr (h) (a): relation3 genv lenv term ≝
-           λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
-           ∀n,T2. ❪G,L1❫ ⊢ T1 ➡[h,n] T2 →
-           ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
+           λG,L1,T1. ❨G,L1❩ ⊢ T1 ![h,a] →
+           ∀n,T2. ❨G,L1❩ ⊢ T1 ➡[h,n] T2 →
+           ∀L2. ❨G,L1❩ ⊢ ➡[h,0] L2 → ❨G,L2❩ ⊢ T2 ![h,a].
 
 definition IH_cnv_cpms_trans_lpr (h) (a): relation3 genv lenv term ≝
-           λG,L1,T1. ❪G,L1❫ ⊢ T1 ![h,a] →
-           ∀n,T2. ❪G,L1❫ ⊢ T1 ➡*[h,n] T2 →
-           ∀L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L2❫ ⊢ T2 ![h,a].
+           λG,L1,T1. ❨G,L1❩ ⊢ T1 ![h,a] →
+           ∀n,T2. ❨G,L1❩ ⊢ T1 ➡*[h,n] T2 →
+           ∀L2. ❨G,L1❩ ⊢ ➡[h,0] L2 → ❨G,L2❩ ⊢ T2 ![h,a].
 
 definition IH_cnv_cpm_conf_lpr (h) (a): relation3 genv lenv term ≝
-           λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
-           ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
-           ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
-           ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
+           λG,L0,T0. ❨G,L0❩ ⊢ T0 ![h,a] →
+           ∀n1,T1. ❨G,L0❩ ⊢ T0 ➡[h,n1] T1 → ∀n2,T2. ❨G,L0❩ ⊢ T0 ➡[h,n2] T2 →
+           ∀L1. ❨G,L0❩ ⊢ ➡[h,0] L1 → ∀L2. ❨G,L0❩ ⊢ ➡[h,0] L2 →
+           ∃∃T. ❨G,L1❩ ⊢ T1 ➡*[h,n2-n1] T & ❨G,L2❩ ⊢ T2 ➡*[h,n1-n2] T.
 
 definition IH_cnv_cpms_strip_lpr (h) (a): relation3 genv lenv term ≝
-           λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
-           ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡[h,n2] T2 →
-           ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
-           ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
+           λG,L0,T0. ❨G,L0❩ ⊢ T0 ![h,a] →
+           ∀n1,T1. ❨G,L0❩ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❨G,L0❩ ⊢ T0 ➡[h,n2] T2 →
+           ∀L1. ❨G,L0❩ ⊢ ➡[h,0] L1 → ∀L2. ❨G,L0❩ ⊢ ➡[h,0] L2 →
+           ∃∃T. ❨G,L1❩ ⊢ T1 ➡*[h,n2-n1] T & ❨G,L2❩ ⊢ T2 ➡*[h,n1-n2] T.
 
 definition IH_cnv_cpms_conf_lpr (h) (a): relation3 genv lenv term ≝
-           λG,L0,T0. ❪G,L0❫ ⊢ T0 ![h,a] →
-           ∀n1,T1. ❪G,L0❫ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❪G,L0❫ ⊢ T0 ➡*[h,n2] T2 →
-           ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G,L0❫ ⊢ ➡[h,0] L2 →
-           ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,n2-n1] T & ❪G,L2❫ ⊢ T2 ➡*[h,n1-n2] T.
+           λG,L0,T0. ❨G,L0❩ ⊢ T0 ![h,a] →
+           ∀n1,T1. ❨G,L0❩ ⊢ T0 ➡*[h,n1] T1 → ∀n2,T2. ❨G,L0❩ ⊢ T0 ➡*[h,n2] T2 →
+           ∀L1. ❨G,L0❩ ⊢ ➡[h,0] L1 → ∀L2. ❨G,L0❩ ⊢ ➡[h,0] L2 →
+           ∃∃T. ❨G,L1❩ ⊢ T1 ➡*[h,n2-n1] T & ❨G,L2❩ ⊢ T2 ➡*[h,n1-n2] T.
 
 (* Auxiliary properties for preservation ************************************)
 
 fact cnv_cpms_trans_lpr_sub (h) (a):
      ∀G0,L0,T0.
-     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
-     ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_trans_lpr h a G1 L1 T1.
+     (∀G1,L1,T1. ❨G0,L0,T0❩ > ❨G1,L1,T1❩ → IH_cnv_cpm_trans_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ❨G0,L0,T0❩ > ❨G1,L1,T1❩ → IH_cnv_cpms_trans_lpr h a G1 L1 T1.
 #h #a #G0 #L0 #T0 #IH #G1 #L1 #T1 #H01 #HT1 #n #T2 #H
 @(cpms_ind_dx … H) -n -T2
 /3 width=7 by fpbg_cpms_trans/
@@ -61,12 +61,12 @@ qed-.
 
 fact cnv_cpm_conf_lpr_sub (h) (a):
      ∀G0,L0,T0.
-     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
-     ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
+     (∀G1,L1,T1. ❨G0,L0,T0❩ > ❨G1,L1,T1❩ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ❨G0,L0,T0❩ > ❨G1,L1,T1❩ → IH_cnv_cpm_conf_lpr h a G1 L1 T1.
 /3 width=8 by cpm_cpms/ qed-.
 
 fact cnv_cpms_strip_lpr_sub (h) (a):
      ∀G0,L0,T0.
-     (∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
-     ∀G1,L1,T1. ❪G0,L0,T0❫ > ❪G1,L1,T1❫ → IH_cnv_cpms_strip_lpr h a G1 L1 T1.
+     (∀G1,L1,T1. ❨G0,L0,T0❩ > ❨G1,L1,T1❩ → IH_cnv_cpms_conf_lpr h a G1 L1 T1) →
+     ∀G1,L1,T1. ❨G0,L0,T0❩ > ❨G1,L1,T1❩ → IH_cnv_cpms_strip_lpr h a G1 L1 T1.
 /3 width=8 by cpm_cpms/ qed-.