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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_cpcs.ma
index ba4b824ce..29d85f7bd 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve_cpcs.ma
@@ -19,20 +19,20 @@ include "basic_2/dynamic/cnv_preserve.ma".
 
 (* Forward lemmas with r-equivalence ****************************************)
 
-lemma cnv_cpms_conf_eq (a) (h) (n) (G) (L):
-      ∀T. ⦃G,L⦄ ⊢ T ![a,h] →
+lemma cnv_cpms_conf_eq (h) (a) (n) (G) (L):
+      ∀T. ⦃G,L⦄ ⊢ T ![h,a] →
       ∀T1. ⦃G,L⦄ ⊢ T ➡*[n,h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ➡*[n,h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2.
-#a #h #n #G #L #T #HT #T1 #HT1 #T2 #HT2
+#h #a #n #G #L #T #HT #T1 #HT1 #T2 #HT2
 elim (cnv_cpms_conf … HT … HT1 … HT2) -T <minus_n_n #T #HT1 #HT2
 /2 width=3 by cprs_div/
 qed-.
 
-lemma cnv_cpms_fwd_appl_sn_decompose (a) (h) (G) (L):
-      ∀V,T. ⦃G,L⦄ ⊢ ⓐV.T ![a,h] → ∀n,X. ⦃G,L⦄ ⊢ ⓐV.T ➡*[n,h] X →
-      ∃∃U. ⦃G,L⦄ ⊢ T ![a,h] & ⦃G,L⦄ ⊢ T ➡*[n,h] U & ⦃G,L⦄ ⊢ ⓐV.U ⬌*[h] X.
-#a #h #G #L #V #T #H0 #n #X #HX
+lemma cnv_cpms_fwd_appl_sn_decompose (h) (a) (G) (L):
+      ∀V,T. ⦃G,L⦄ ⊢ ⓐV.T ![h,a] → ∀n,X. ⦃G,L⦄ ⊢ ⓐV.T ➡*[n,h] X →
+      ∃∃U. ⦃G,L⦄ ⊢ T ![h,a] & ⦃G,L⦄ ⊢ T ➡*[n,h] U & ⦃G,L⦄ ⊢ ⓐV.U ⬌*[h] X.
+#h #a #G #L #V #T #H0 #n #X #HX
 elim (cnv_inv_appl … H0) #m #p #W #U #_ #_ #HT #_ #_ -m -p -W -U
-elim (cnv_fwd_cpms_total … h n … HT) #U #HTU
+elim (cnv_fwd_cpms_total h … n … HT) #U #HTU
 lapply (cpms_appl_dx … V V … HTU) [ // ] #H
 /3 width=8 by cnv_cpms_conf_eq, ex3_intro/
 qed-.