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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
index 96c53c7db..0edc5d3b1 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
@@ -12,37 +12,50 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lex_tc.ma".
-include "basic_2/rt_computation/cprs_lpr.ma".
-include "basic_2/rt_computation/lprs.ma".
+include "basic_2/rt_computation/lprs_tc.ma".
 
 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
 
 (* Eliminators with r-transition for full local environments ****************)
 
 (* Basic_2A1: was: lprs_ind_dx *)
-lemma lprs_ind_sn (h) (G) (L2): ∀R:predicate lenv. R L2 →
-                                (∀L1,L. ⦃G, L1⦄ ⊢ ➡[h] L → ⦃G, L⦄ ⊢ ➡*[h] L2 → R L → R L1) →
-                                ∀L1. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R L1.
-/3 width=7 by lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
+lemma lprs_ind_sn (h) (G) (L2):
+      ∀Q:predicate lenv. Q L2 →
+      (∀L1,L. ❪G,L1❫ ⊢ ➡[h,0] L → ❪G,L❫ ⊢ ➡*[h,0] L2 → Q L → Q L1) →
+      ∀L1. ❪G,L1❫ ⊢ ➡*[h,0] L2 → Q L1.
+/4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
 
 (* Basic_2A1: was: lprs_ind *)
-lemma lprs_ind_dx (h) (G) (L1): ∀R:predicate lenv. R L1 →
-                                (∀L,L2. ⦃G, L1⦄ ⊢ ➡*[h] L → ⦃G, L⦄ ⊢ ➡[h] L2 → R L → R L2) →
-                                ∀L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R L2.
-/3 width=7 by lpr_cprs_trans, cpr_refl, lex_CTC_ind_dx/ qed-.
+lemma lprs_ind_dx (h) (G) (L1):
+      ∀Q:predicate lenv. Q L1 →
+      (∀L,L2. ❪G,L1❫ ⊢ ➡*[h,0] L → ❪G,L❫ ⊢ ➡[h,0] L2 → Q L → Q L2) →
+      ∀L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 → Q L2.
+/4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_dx/ qed-.
 
-(* Properties with unbound rt-transition for full local environments ********)
+(* Properties with extended rt-transition for full local environments *******)
 
-lemma lpr_lprs (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
-/3 width=3 by lpr_cprs_trans, lex_CTC_inj/ qed.
+lemma lpr_lprs (h) (G):
+      ∀L1,L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
+/4 width=3 by lprs_CTC, lpr_cprs_trans, lex_CTC_inj/ qed.
 
 (* Basic_2A1: was: lprs_strap2 *)
-lemma lprs_step_sn (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡[h] L →
-                            ∀L2.⦃G, L⦄ ⊢ ➡*[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
-/3 width=3 by lpr_cprs_trans, lex_CTC_step_sn/ qed-.
+lemma lprs_step_sn (h) (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ➡[h,0] L →
+      ∀L2.❪G,L❫ ⊢ ➡*[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
+/4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_strap1 *)
-lemma lprs_step_dx (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡*[h] L →
-                            ∀L2. ⦃G, L⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
-/3 width=3 by lpr_cprs_trans, lex_CTC_step_dx/ qed-.
+lemma lprs_step_dx (h) (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ➡*[h,0] L →
+      ∀L2. ❪G,L❫ ⊢ ➡[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
+/4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_dx/ qed-.
+
+lemma lprs_strip (h) (G):
+      confluent2 … (lprs h 0 G) (lpr h 0 G).
+#h #G #L0 #L1 #HL01 #L2 #HL02
+elim (TC_strip1 … L1 ?? HL02) -HL02
+[ /3 width=3 by lprs_TC, ex2_intro/ | skip
+| /2 width=1 by lprs_inv_TC/
+| /2 width=3 by lpr_conf/
+]
+qed-.