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diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
index 6f8e3bc74..cc3e75b0a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
@@ -12,18 +12,18 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazyeq_3.ma".
-include "basic_2/syntax/ext2.ma".
+include "basic_2/notation/relations/lazyeqsn_3.ma".
+include "basic_2/syntax/ceq_ext.ma".
 include "basic_2/relocation/lexs.ma".
 
 (* RANGED EQUIVALENCE FOR LOCAL ENVIRONMENTS ********************************)
 
 (* Basic_2A1: includes: lreq_atom lreq_zero lreq_pair lreq_succ *)
-definition lreq: relation3 rtmap lenv lenv ≝ lexs ceq cfull.
+definition lreq: relation3 rtmap lenv lenv ≝ lexs ceq_ext cfull.
 
 interpretation
   "ranged equivalence (local environment)"
-  'LazyEq f L1 L2 = (lreq f L1 L2).
+  'LazyEqSn f L1 L2 = (lreq f L1 L2).
 
 (* Basic properties *********************************************************)
 
@@ -39,11 +39,11 @@ lemma sle_lreq_trans: ∀f2,L1,L2. L1 ≡[f2] L2 →
 
 (* Basic_2A1: includes: lreq_refl *)
 lemma lreq_refl: ∀f. reflexive … (lreq f).
-/3 width=1 by lexs_refl, ext2_refl/ qed.
+/2 width=1 by lexs_refl/ qed.
 
 (* Basic_2A1: includes: lreq_sym *)
 lemma lreq_sym: ∀f. symmetric … (lreq f).
-/3 width=1 by lexs_sym, ext2_sym/ qed-.
+/3 width=2 by lexs_sym, cext2_sym/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
@@ -54,7 +54,9 @@ lemma lreq_inv_atom1: ∀f,Y. ⋆ ≡[f] Y → Y = ⋆.
 (* Basic_2A1: includes: lreq_inv_pair1 *)
 lemma lreq_inv_next1: ∀g,J,K1,Y. K1.ⓘ{J} ≡[⫯g] Y →
                       ∃∃K2. K1 ≡[g] K2 & Y = K2.ⓘ{J}.
-#g #J #K1 #Y #H elim (lexs_inv_next1 … H) -H /2 width=3 by ex2_intro/
+#g #J #K1 #Y #H
+elim (lexs_inv_next1 … H) -H #Z #K2 #HK12 #H1 #H2 destruct
+<(ceq_ext_inv_eq … H1) -Z /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_zero1 lreq_inv_succ1 *)
@@ -70,7 +72,9 @@ lemma lreq_inv_atom2: ∀f,X. X ≡[f] ⋆ → X = ⋆.
 (* Basic_2A1: includes: lreq_inv_pair2 *)
 lemma lreq_inv_next2: ∀g,J,X,K2. X ≡[⫯g] K2.ⓘ{J} →
                       ∃∃K1. K1 ≡[g] K2 & X = K1.ⓘ{J}.
-#g #J #X #K2 #H elim (lexs_inv_next2 … H) -H /2 width=3 by ex2_intro/
+#g #J #X #K2 #H
+elim (lexs_inv_next2 … H) -H #Z #K1 #HK12 #H1 #H2 destruct
+<(ceq_ext_inv_eq … H1) -J /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_zero2 lreq_inv_succ2 *)
@@ -82,7 +86,9 @@ qed-.
 (* Basic_2A1: includes: lreq_inv_pair *)
 lemma lreq_inv_next: ∀f,I1,I2,L1,L2. L1.ⓘ{I1} ≡[⫯f] L2.ⓘ{I2} →
                      L1 ≡[f] L2 ∧ I1 = I2.
-/2 width=1 by lexs_inv_next/ qed-.
+#f #I1 #I2 #L1 #L2 #H elim (lexs_inv_next … H) -H
+/3 width=3 by ceq_ext_inv_eq, conj/
+qed-.
 
 (* Basic_2A1: includes: lreq_inv_succ *)
 lemma lreq_inv_push: ∀f,I1,I2,L1,L2. L1.ⓘ{I1} ≡[↑f] L2.ⓘ{I2} → L1 ≡[f] L2.