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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqg.ma
index 4041da979..7dbb2b0d5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqg.ma
@@ -12,22 +12,22 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/static/req.ma".
-include "basic_2/rt_transition/rpx_lpx.ma".
+include "basic_2/rt_transition/rpx_lpx.ma". (**) (* one dependence *)
 
 (* EXTENDED PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS **************)
 
 (* Properties with generic equivalence for local environments ***************)
 
 lemma reqg_lpx_trans_rpx (S) (G) (L) (T:term):
-      ∀L1. L1 ≛[S,T] L → ∀L2. ❪G,L❫ ⊢ ⬈ L2 → ❪G,L❫ ⊢ ⬈[T] L2.
-/3 width=1 by lpx_rpx, reqg_rpx_trans/ qed.
+      reflexive … S → symmetric … S →
+      ∀L1. L1 ≛[S,T] L → ∀L2. ❨G,L❩ ⊢ ⬈ L2 → ❨G,L1❩ ⊢ ⬈[T] L2.
+/3 width=6 by lpx_rpx, reqg_rpx_trans/ qed.
 
 (* Basic_2A1: uses: lleq_lpx_trans *)
 lemma reqg_lpx_trans (S) (G) (T:term):
       reflexive … S → symmetric … S →
-      ∀L2,K2. ❪G,L2❫ ⊢ ⬈ K2 → ∀L1. L1 ≛[S,T] L2 →
-      ∃∃K1. ❪G,L1❫ ⊢ ⬈ K1 & K1 ≛[S,T] K2.
+      ∀L2,K2. ❨G,L2❩ ⊢ ⬈ K2 → ∀L1. L1 ≛[S,T] L2 →
+      ∃∃K1. ❨G,L1❩ ⊢ ⬈ K1 & K1 ≛[S,T] K2.
 #S #G #T #H1S #H2S #L2 #K2 #HLK2 #L1 #HL12
 lapply (lpx_rpx … T … HLK2) -HLK2 #HLK2
 lapply (reqg_rpx_trans … HL12 … HLK2) -L2 // #H
@@ -35,23 +35,23 @@ elim (rpx_fwd_lpx_req … H) -H #K1 #HLK1 #HK12
 /3 width=3 by req_fwd_reqg, ex2_intro/
 qed-.
 
-(* Inversion lemmas with sort-irrelevant equivalence for local environments *)
+(* Inversion lemmas with generic equivalence for local environments *********)
 
 lemma rpx_inv_reqg_lpx (S) (G) (T):
       reflexive … S →
-      ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
-      ∃∃L. L1 ≛[S,T] L & ❪G,L❫ ⊢ ⬈ L2.
+      ∀L1,L2. ❨G,L1❩ ⊢ ⬈[T] L2 →
+      ∃∃L. L1 ≛[S,T] L & ❨G,L❩ ⊢ ⬈ L2.
 #S #G #T #HS #L1 #L2 #H
 elim (rpx_inv_req_lpx … H) -H #L #HL1 #HL2
 /3 width=3 by req_fwd_reqg, ex2_intro/
 qed-.
 
-(* Forward lemmas with sort-irrelevant equivalence for local environments ***)
+(* Forward lemmas with generic equivalence for local environments ***********)
 
 lemma rpx_fwd_lpx_reqg (S) (G) (T):
       reflexive … S →
-      ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
-      ∃∃L. ❪G,L1❫ ⊢ ⬈ L & L ≛[S,T] L2.
+      ∀L1,L2. ❨G,L1❩ ⊢ ⬈[T] L2 →
+      ∃∃L. ❨G,L1❩ ⊢ ⬈ L & L ≛[S,T] L2.
 #S #G #T #HS #L1 #L2 #H
 elim (rpx_fwd_lpx_req … H) -H #L #HL1 #HL2
 /3 width=3 by req_fwd_reqg, ex2_intro/