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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmuwe.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmuwe.ma
index 011388942..ce73661f8 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmuwe.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpmuwe.ma
@@ -18,27 +18,25 @@ include "basic_2/dynamic/cnv_preserve.ma".
 
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
-(* Properties with head evaluation for t-bound rt-transition on terms *******)
+(* Properties with t-unbound whd evaluation on terms ************************)
 
-lemma cnv_cpmuwe_trans (a) (h) (G) (L):
-      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
-      ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ⦃G,L⦄ ⊢ T2 ![a,h].
+lemma cnv_cpmuwe_trans (h) (a) (G) (L):
+      ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
+      ∀n,T2. ❪G,L❫ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ❪G,L❫ ⊢ T2 ![h,a].
 /3 width=4 by cpmuwe_fwd_cpms, cnv_cpms_trans/ qed-.
 
-lemma cnv_R_cpmuwe_total (a) (h) (G) (L):
-      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∃n. R_cpmuwe h G L T1 n.
+lemma cnv_R_cpmuwe_total (h) (a) (G) (L):
+      ∀T1. ❪G,L❫ ⊢ T1 ![h,a] → ∃n. R_cpmuwe h G L T1 n.
 /4 width=2 by cnv_fwd_fsb, fsb_inv_csx, R_cpmuwe_total_csx/ qed-.
 
-axiom cnv_R_cpmuwe_dec (a) (h) (G) (L):
-      ∀T. ⦃G,L⦄ ⊢ T ![a,h] → ∀n. Decidable (R_cpmuwe h G L T n).
-
 (* Main inversions with head evaluation for t-bound rt-transition on terms **)
 
-theorem cnv_cpmuwe_mono (a) (h) (G) (L):
-        ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
-        ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
-        ∧∧ ⦃G,L⦄ ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≅ T2.
-#a #h #G #L #T0 #HT0 #T1 #n1 * #HT01 #HT1 #T2 #n2 * #HT02 #HT2
+theorem cnv_cpmuwe_mono (h) (a) (G) (L):
+        ∀T0. ❪G,L❫ ⊢ T0 ![h,a] →
+        ∀n1,T1. ❪G,L❫ ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
+        ∀n2,T2. ❪G,L❫ ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
+        ∧∧ ❪G,L❫ ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≅ T2.
+#h #a #G #L #T0 #HT0 #n1 #T1 * #HT01 #HT1 #n2 #T2 * #HT02 #HT2
 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
 /4 width=4 by cpms_div, tweq_canc_dx, conj/
 qed-.