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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_trans.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_trans.ma
index 2ff1bbb6d..8c50c3a7e 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_trans.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_trans.ma
@@ -19,14 +19,14 @@ include "basic_2/dynamic/cnv_cpm_teqx.ma".
 
 definition IH_cnv_cpm_teqx_cpm_trans (h) (a): relation3 genv lenv term ≝
            λG,L,T1. ❪G,L❫ ⊢ T1 ![h,a] →
-           ∀n1,T. ❪G,L❫ ⊢ T1 ➡[n1,h] T → T1 ≛ T →
-           ∀n2,T2. ❪G,L❫ ⊢ T ➡[n2,h] T2 →
-           ∃∃T0. ❪G,L❫ ⊢ T1 ➡[n2,h] T0 & ❪G,L❫ ⊢ T0 ➡[n1,h] T2 & T0 ≛ T2.
+           ∀n1,T. ❪G,L❫ ⊢ T1 ➡[h,n1] T → T1 ≛ T →
+           ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 →
+           ∃∃T0. ❪G,L❫ ⊢ T1 ➡[h,n2] T0 & ❪G,L❫ ⊢ T0 ➡[h,n1] T2 & T0 ≛ T2.
 
 (* Transitive properties restricted rt-transition for terms *****************)
 
 fact cnv_cpm_teqx_cpm_trans_sub (h) (a) (G0) (L0) (T0):
-     (∀G,L,T. ❪G0,L0,T0❫ >[h] ❪G,L,T❫ → IH_cnv_cpm_trans_lpr h a G L T) →
+     (∀G,L,T. ❪G0,L0,T0❫ > ❪G,L,T❫ → IH_cnv_cpm_trans_lpr h a G L T) →
      (∀G,L,T. ❪G0,L0,T0❫ ⬂+ ❪G,L,T❫ → IH_cnv_cpm_teqx_cpm_trans h a G L T) →
      ∀G,L,T1. G0 = G → L0 = L → T0 = T1 → IH_cnv_cpm_teqx_cpm_trans h a G L T1.
 #h #a #G0 #L0 #T0 #IH2 #IH1 #G #L * [| * [| * ]]
@@ -89,7 +89,7 @@ fact cnv_cpm_teqx_cpm_trans_sub (h) (a) (G0) (L0) (T0):
 qed-.
 
 fact cnv_cpm_teqx_cpm_trans_aux (h) (a) (G0) (L0) (T0):
-     (∀G,L,T. ❪G0,L0,T0❫ >[h] ❪G,L,T❫ → IH_cnv_cpm_trans_lpr h a G L T) →
+     (∀G,L,T. ❪G0,L0,T0❫ > ❪G,L,T❫ → IH_cnv_cpm_trans_lpr h a G L T) →
      IH_cnv_cpm_teqx_cpm_trans h a G0 L0 T0.
 #h #a #G0 #L0 #T0
 @(fqup_wf_ind (Ⓣ) … G0 L0 T0) -G0 -L0 -T0 #G0 #L0 #T0 #IH #IH0