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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_teqx_conf.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_teqx_conf.ma
index 24a56092c..5fa5e07d4 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_teqx_conf.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_teqx_conf.ma
@@ -22,10 +22,10 @@ include "basic_2/dynamic/cnv_cpms_teqx.ma".
 fact cnv_cpms_teqx_strip_lpr_aux (h) (a) (G0) (L0) (T0):
      (∀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_cpms_conf_lpr h a G L T) →
-     ∀n1,T1. ❪G0,L0❫ ⊢ T0 ➡*[h,n1] T1 → ❪G0,L0❫ ⊢ T0 ![h,a] → T0 ≛ T1 →
-     ∀n2,T2. ❪G0,L0❫ ⊢ T0 ➡[h,n2] T2 → T0 ≛ T2 →
+     ∀n1,T1. ❪G0,L0❫ ⊢ T0 ➡*[h,n1] T1 → ❪G0,L0❫ ⊢ T0 ![h,a] → T0 ≅ T1 →
+     ∀n2,T2. ❪G0,L0❫ ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
      ∀L1. ❪G0,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G0,L0❫ ⊢ ➡[h,0] L2 →
-     ∃∃T. ❪G0,L1❫ ⊢ T1 ➡[h,n2-n1] T & T1 ≛ T & ❪G0,L2❫ ⊢ T2 ➡*[h,n1-n2] T & T2 ≛ T.
+     ∃∃T. ❪G0,L1❫ ⊢ T1 ➡[h,n2-n1] T & T1 ≅ T & ❪G0,L2❫ ⊢ T2 ➡*[h,n1-n2] T & T2 ≅ T.
 #h #a #G #L0 #T0 #IH2 #IH1 #n1 #T1 #H1T01 #H0T0 #H2T01
 @(cpms_teqx_ind_sn … H1T01 H0T0 H2T01 IH1 IH2) -n1 -T0
 [ #H0T1 #n2 #T2 #H1T12 #H2T12 #L1 #HL01 #L2 #HL02
@@ -47,10 +47,10 @@ qed-.
 fact cnv_cpms_teqx_conf_lpr_aux (h) (a) (G0) (L0) (T0):
      (∀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_cpms_conf_lpr h a G L T) →
-     ∀n1,T1. ❪G0,L0❫ ⊢ T0 ➡*[h,n1] T1 → ❪G0,L0❫ ⊢ T0 ![h,a] → T0 ≛ T1 →
-     ∀n2,T2. ❪G0,L0❫ ⊢ T0 ➡*[h,n2] T2 → T0 ≛ T2 →
+     ∀n1,T1. ❪G0,L0❫ ⊢ T0 ➡*[h,n1] T1 → ❪G0,L0❫ ⊢ T0 ![h,a] → T0 ≅ T1 →
+     ∀n2,T2. ❪G0,L0❫ ⊢ T0 ➡*[h,n2] T2 → T0 ≅ T2 →
      ∀L1. ❪G0,L0❫ ⊢ ➡[h,0] L1 → ∀L2. ❪G0,L0❫ ⊢ ➡[h,0] L2 →
-     ∃∃T. ❪G0,L1❫ ⊢ T1 ➡*[h,n2-n1] T & T1 ≛ T & ❪G0,L2❫ ⊢ T2 ➡*[h,n1-n2] T & T2 ≛ T.
+     ∃∃T. ❪G0,L1❫ ⊢ T1 ➡*[h,n2-n1] T & T1 ≅ T & ❪G0,L2❫ ⊢ T2 ➡*[h,n1-n2] T & T2 ≅ T.
 #h #a #G #L0 #T0 #IH2 #IH1 #n1 #T1 #H1T01 #H0T0 #H2T01
 generalize in match IH1; generalize in match IH2;
 @(cpms_teqx_ind_sn … H1T01 H0T0 H2T01 IH1 IH2) -n1 -T0