From cac628104788b9400cc1a33407272fd4c35f2402 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 7 Aug 2013 14:44:32 +0000
Subject: [PATCH] partial commit: "conversion" and "equivalence" components ...

---
 .../lambdadelta/basic_2/conversion/cpc.ma     |  20 +--
 .../lambdadelta/basic_2/conversion/cpc_cpc.ma |   4 +-
 .../lambdadelta/basic_2/equivalence/cpcs.ma   |  45 +++---
 .../basic_2/equivalence/cpcs_aaa.ma           |   4 +-
 .../basic_2/equivalence/cpcs_cpcs.ma          | 128 ++++++++++--------
 .../basic_2/equivalence/cpcs_cprs.ma          |  32 ++---
 .../relations/{pconv_3.ma => pconv_4.ma}      |   4 +-
 .../{pconvstar_3.ma => pconvstar_4.ma}        |   4 +-
 .../lambdadelta/basic_2/web/basic_2_src.tbl   |  12 +-
 9 files changed, 131 insertions(+), 122 deletions(-)
 rename matita/matita/contribs/lambdadelta/basic_2/notation/relations/{pconv_3.ma => pconv_4.ma} (89%)
 rename matita/matita/contribs/lambdadelta/basic_2/notation/relations/{pconvstar_3.ma => pconvstar_4.ma} (89%)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma
index 5be5601ea..116e15950 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma
@@ -12,29 +12,29 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/pconv_3.ma".
+include "basic_2/notation/relations/pconv_4.ma".
 include "basic_2/reduction/cpr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
 
-definition cpc: lenv → relation term ≝
-   λL,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1.
+definition cpc: relation4 genv lenv term term ≝
+                λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1.
 
 interpretation
    "context-sensitive parallel conversion (term)"
-   'PConv L T1 T2 = (cpc L T1 T2).
+   'PConv G L T1 T2 = (cpc G L T1 T2).
 
 (* Basic properties *********************************************************)
 
-lemma cpc_refl: ∀L. reflexive … (cpc L).
+lemma cpc_refl: ∀G,L. reflexive … (cpc G L).
 /2 width=1/ qed.
 
-lemma cpc_sym: ∀L. symmetric … (cpc L).
-#L #T1 #T2 * /2 width=1/
+lemma cpc_sym: ∀G,L. symmetric … (cpc L G).
+#G #L #T1 #T2 * /2 width=1/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma cpc_fwd_cpr: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T.
-#L #T1 #T2 * /2 width=3/
-qed.
+lemma cpc_fwd_cpr: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T.
+#G #L #T1 #T2 * /2 width=3/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma
index 092d2a9a7..714d3e712 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/conversion/cpc_cpc.ma
@@ -18,6 +18,6 @@ include "basic_2/conversion/cpc.ma".
 
 (* Main properties **********************************************************)
 
-theorem cpc_conf: ∀L,T0,T1,T2. ⦃G, L⦄ ⊢ T0 ⬌ T1 → ⦃G, L⦄ ⊢ T0 ⬌ T2 →
+theorem cpc_conf: ∀G,L,T0,T1,T2. ⦃G, L⦄ ⊢ T0 ⬌ T1 → ⦃G, L⦄ ⊢ T0 ⬌ T2 →
                   ∃∃T. ⦃G, L⦄ ⊢ T1 ⬌ T & ⦃G, L⦄ ⊢ T2 ⬌ T.
-/3 width=3/ qed.
+/3 width=3/ qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
index a7e5b7514..deb838412 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
@@ -12,73 +12,74 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/pconvstar_3.ma".
+include "basic_2/notation/relations/pconvstar_4.ma".
 include "basic_2/conversion/cpc.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
 
-definition cpcs: lenv → relation term ≝ LTC … cpc.
+definition cpcs: relation4 genv lenv term term ≝
+           λG. LTC … (cpc G).
 
 interpretation "context-sensitive parallel equivalence (term)"
-   'PConvStar L T1 T2 = (cpcs L T1 T2).
+   'PConvStar G L T1 T2 = (cpcs G L T1 T2).
 
 (* Basic eliminators ********************************************************)
 
-lemma cpcs_ind: ∀L,T1. ∀R:predicate term. R T1 →
+lemma cpcs_ind: ∀G,L,T1. ∀R:predicate term. R T1 →
                 (∀T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → R T → R T2) →
                 ∀T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → R T2.
-#L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
+#G #L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
 qed-.
 
-lemma cpcs_ind_dx: ∀L,T2. ∀R:predicate term. R T2 →
+lemma cpcs_ind_dx: ∀G,L,T2. ∀R:predicate term. R T2 →
                    (∀T1,T. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → R T → R T1) →
                    ∀T1. ⦃G, L⦄ ⊢ T1 ⬌* T2 → R T1.
-#L #T2 #R #HT2 #IHT2 #T1 #HT12
+#G #L #T2 #R #HT2 #IHT2 #T1 #HT12
 @(TC_star_ind_dx … HT2 IHT2 … HT12) //
 qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: pc3_refl *)
-lemma cpcs_refl: ∀L. reflexive … (cpcs L).
+lemma cpcs_refl: ∀G,L. reflexive … (cpcs G L).
 /2 width=1/ qed.
 
 (* Basic_1: was: pc3_s *)
-lemma cpcs_sym: ∀L. symmetric … (cpcs L).
-#L @TC_symmetric // qed.
+lemma cpcs_sym: ∀G,L. symmetric … (cpcs G L).
+#G #L @TC_symmetric // qed.
 
-lemma cpc_cpcs: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T2.
+lemma cpc_cpcs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T2.
 /2 width=1/ qed.
 
-lemma cpcs_strap1: ∀L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L @step qed.
+lemma cpcs_strap1: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L @step qed.
 
-lemma cpcs_strap2: ∀L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L @TC_strap qed.
+lemma cpcs_strap2: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L @TC_strap qed.
 
 (* Basic_1: was: pc3_pr2_r *)
-lemma cpr_cpcs_dx: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpr_cpcs_dx: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=1/ qed.
 
 (* Basic_1: was: pc3_pr2_x *)
-lemma cpr_cpcs_sn: ∀L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡ T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpr_cpcs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡ T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=1/ qed.
 
-lemma cpcs_cpr_strap1: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpcs_cpr_strap1: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3/ qed.
 
 (* Basic_1: was: pc3_pr2_u *)
-lemma cpcs_cpr_strap2: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpcs_cpr_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3/ qed.
 
-lemma cpcs_cpr_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpcs_cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3/ qed.
 
-lemma cpr_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3/ qed-.
 
 (* Basic_1: was: pc3_pr2_u2 *)
-lemma cpcs_cpr_conf: ∀L,T1,T. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpcs_cpr_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3/ qed.
 
 (* Basic_1: removed theorems 9:
diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma
index 1a5e48687..ce4bf678e 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_aaa.ma
@@ -19,10 +19,10 @@ include "basic_2/equivalence/cpcs_cpcs.ma".
 
 (* Main properties about atomic arity assignment on terms *******************)
 
-theorem aaa_cpcs_mono: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
+theorem aaa_cpcs_mono: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
                        ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 →
                        A1 = A2.
-#L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
+#G #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
 lapply (aaa_cprs_conf … HA1 … HT1) -T1 #HA1
 lapply (aaa_cprs_conf … HA2 … HT2) -T2 #HA2
diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
index 125cc70fe..e6ef1a9ad 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
@@ -20,9 +20,9 @@ include "basic_2/equivalence/cpcs_cprs.ma".
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpcs_inv_cprs: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
+lemma cpcs_inv_cprs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
                      ∃∃T. ⦃G, L⦄ ⊢ T1 ➡* T & ⦃G, L⦄ ⊢ T2 ➡* T.
-#L #T1 #T2 #H @(cpcs_ind … H) -T2
+#G #L #T1 #T2 #H @(cpcs_ind … H) -T2
 [ /3 width=3/
 | #T #T2 #_ #HT2 * #T0 #HT10 elim HT2 -HT2 #HT2 #HT0
   [ elim (cprs_strip … HT0 … HT2) -T #T #HT0 #HT2
@@ -33,38 +33,38 @@ lemma cpcs_inv_cprs: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
 qed-.
 
 (* Basic_1: was: pc3_gen_sort *)
-lemma cpcs_inv_sort: ∀L,k1,k2. ⦃G, L⦄ ⊢ ⋆k1 ⬌* ⋆k2 → k1 = k2.
-#L #k1 #k2 #H
+lemma cpcs_inv_sort: ∀G,L,k1,k2. ⦃G, L⦄ ⊢ ⋆k1 ⬌* ⋆k2 → k1 = k2.
+#G #L #k1 #k2 #H
 elim (cpcs_inv_cprs … H) -H #T #H1
 >(cprs_inv_sort1 … H1) -T #H2
 lapply (cprs_inv_sort1 … H2) -L #H destruct //
 qed-.
 
-lemma cpcs_inv_abst1: ∀a,L,W1,T1,T. ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ⬌* T →
+lemma cpcs_inv_abst1: ∀a,G,L,W1,T1,T. ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ⬌* T →
                       ∃∃W2,T2. ⦃G, L⦄ ⊢ T ➡* ⓛ{a}W2.T2 & ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ➡* ⓛ{a}W2.T2.
-#a #L #W1 #T1 #T #H
+#a #G #L #W1 #T1 #T #H
 elim (cpcs_inv_cprs … H) -H #X #H1 #H2
 elim (cprs_inv_abst1 … H1) -H1 #W2 #T2 #HW12 #HT12 #H destruct
 @(ex2_2_intro … H2) -H2 /2 width=2/ (**) (* explicit constructor, /3 width=6/ is slow *)
 qed-.
 
-lemma cpcs_inv_abst2: ∀a,L,W1,T1,T. ⦃G, L⦄ ⊢ T ⬌* ⓛ{a}W1.T1 →
+lemma cpcs_inv_abst2: ∀a,G,L,W1,T1,T. ⦃G, L⦄ ⊢ T ⬌* ⓛ{a}W1.T1 →
                       ∃∃W2,T2. ⦃G, L⦄ ⊢ T ➡* ⓛ{a}W2.T2 & ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ➡* ⓛ{a}W2.T2.
 /3 width=1 by cpcs_inv_abst1, cpcs_sym/ qed-.
 
 (* Basic_1: was: pc3_gen_sort_abst *)
-lemma cpcs_inv_sort_abst: ∀a,L,W,T,k. ⦃G, L⦄ ⊢ ⋆k ⬌* ⓛ{a}W.T → ⊥.
-#a #L #W #T #k #H
+lemma cpcs_inv_sort_abst: ∀a,G,L,W,T,k. ⦃G, L⦄ ⊢ ⋆k ⬌* ⓛ{a}W.T → ⊥.
+#a #G #L #W #T #k #H
 elim (cpcs_inv_cprs … H) -H #X #H1
 >(cprs_inv_sort1 … H1) -X #H2
 elim (cprs_inv_abst1 … H2) -H2 #W0 #T0 #_ #_ #H destruct
 qed-.
 
 (* Basic_1: was: pc3_gen_lift *)
-lemma cpcs_inv_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+lemma cpcs_inv_lift: ∀G,L,K,d,e. ⇩[d, e] L ≡ K →
                      ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 →
-                     ⦃G, L⦄ ⊢ U1 ⬌* U2 → K ⊢ T1 ⬌* T2.
-#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12
+                     ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, K⦄ ⊢ T1 ⬌* T2.
+#G #L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12
 elim (cpcs_inv_cprs … HU12) -HU12 #U #HU1 #HU2
 elim (cprs_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HTU #HT1
 elim (cprs_inv_lift1 … HU2 … HLK … HTU2) -L -U2 #X #HXU
@@ -73,100 +73,105 @@ qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma lpr_cpcs_trans: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H
+lemma lpr_cpcs_trans: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                      ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ⬌* T2 → ⦃G, L1⦄ ⊢ T1 ⬌* T2.
+#G #L1 #L2 #HL12 #T1 #T2 #H
 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
 lapply (lpr_cprs_trans … HT1 … HL12) -HT1
 lapply (lpr_cprs_trans … HT2 … HL12) -L2 /2 width=3/
 qed-.
 
-lemma lprs_cpcs_trans: ∀L1,L2. L1 ⊢ ➡* L2 → ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H
+lemma lprs_cpcs_trans: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 →
+                       ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ⬌* T2 → ⦃G, L1⦄ ⊢ T1 ⬌* T2.
+#G #L1 #L2 #HL12 #T1 #T2 #H
 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
 lapply (lprs_cprs_trans … HT1 … HL12) -HT1
 lapply (lprs_cprs_trans … HT2 … HL12) -L2 /2 width=3/
 qed-.
 
-lemma cpr_cprs_conf_cpcs: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T #T1 #T2 #HT1 #HT2
+lemma cpr_cprs_conf_cpcs: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T #T1 #T2 #HT1 #HT2
 elim (cprs_strip … HT1 … HT2) /2 width=3 by cpr_cprs_div/
 qed-.
 
-lemma cprs_cpr_conf_cpcs: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T1.
-#L #T #T1 #T2 #HT1 #HT2
+lemma cprs_cpr_conf_cpcs: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T2 ⬌* T1.
+#G #L #T #T1 #T2 #HT1 #HT2
 elim (cprs_strip … HT1 … HT2) /2 width=3 by cprs_cpr_div/
 qed-.
 
-lemma cprs_conf_cpcs: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T #T1 #T2 #HT1 #HT2
+lemma cprs_conf_cpcs: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ➡* T1 → ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T #T1 #T2 #HT1 #HT2
 elim (cprs_conf … HT1 … HT2) /2 width=3/
 qed-.
 
-lemma lprs_cprs_conf: ∀L1,L2. L1 ⊢ ➡* L2 → ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #HT12
+lemma lprs_cprs_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 →
+                      ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
+#G #L1 #L2 #HL12 #T1 #T2 #HT12
 elim (lprs_cprs_conf_dx … HT12 … HL12) -L1 /2 width=3/
 qed-.
 
 (* Basic_1: was: pc3_wcpr0_t *)
 (* Basic_1: note: pc3_wcpr0_t should be renamed *)
-lemma lpr_cprs_conf: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡* T2 → L2 ⊢ T1 ⬌* T2.
+lemma lpr_cprs_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                     ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
 /3 width=5 by lprs_cprs_conf, lpr_lprs/ qed-.
 
 (* Basic_1: was only: pc3_pr0_pr2_t *)
 (* Basic_1: note: pc3_pr0_pr2_t should be renamed *)
-lemma lpr_cpr_conf: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡ T2 → L2 ⊢ T1 ⬌* T2.
+lemma lpr_cpr_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                    ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
 /3 width=5 by lpr_cprs_conf, cpr_cprs/ qed-.
 
 (* Basic_1: was only: pc3_thin_dx *)
-lemma cpcs_flat: ∀L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
-                 ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1. T1 ⬌* ⓕ{I}V2. T2.
-#L #V1 #V2 #HV12 #T1 #T2 #HT12 #I
+lemma cpcs_flat: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
+                 ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ⬌* ⓕ{I}V2.T2.
+#G #L #V1 #V2 #HV12 #T1 #T2 #HT12 #I
 elim (cpcs_inv_cprs … HV12) -HV12 #V #HV1 #HV2
 elim (cpcs_inv_cprs … HT12) -HT12 /3 width=5 by cprs_flat, cprs_div/ (**) (* /3 width=5/ is too slow *)
 qed.
 
-lemma cpcs_flat_dx_cpr_rev: ∀L,V1,V2. ⦃G, L⦄ ⊢ V2 ➡ V1 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
-                            ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1. T1 ⬌* ⓕ{I}V2. T2.
+lemma cpcs_flat_dx_cpr_rev: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V2 ➡ V1 → ∀T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
+                            ∀I. ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ⬌* ⓕ{I}V2.T2.
 /3 width=1/ qed.
 
-lemma cpcs_bind_dx: ∀a,I,L,V,T1,T2. L.ⓑ{I}V ⊢ T1 ⬌* T2 →
-                    ⦃G, L⦄ ⊢ ⓑ{a,I}V. T1 ⬌* ⓑ{a,I}V. T2.
-#a #I #L #V #T1 #T2 #HT12
+lemma cpcs_bind_dx: ∀a,I,G,L,V,T1,T2. ⦃G, L.ⓑ{I}V⦄ ⊢ T1 ⬌* T2 →
+                    ⦃G, L⦄ ⊢ ⓑ{a,I}V.T1 ⬌* ⓑ{a,I}V.T2.
+#a #I #G #L #V #T1 #T2 #HT12
 elim (cpcs_inv_cprs … HT12) -HT12 /3 width=5 by cprs_div, cprs_bind/ (**) (* /3 width=5/ is a bit slow *)
 qed.
 
-lemma cpcs_bind_sn: ∀a,I,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T ⬌* ⓑ{a,I}V2. T.
-#a #I #L #V1 #V2 #T #HV12
+lemma cpcs_bind_sn: ∀a,I,G,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T ⬌* ⓑ{a,I}V2. T.
+#a #I #G #L #V1 #V2 #T #HV12
 elim (cpcs_inv_cprs … HV12) -HV12 /3 width=5 by cprs_div, cprs_bind/ (**) (* /3 width=5/ is a bit slow *)
 qed.
 
-lemma lsubr_cpcs_trans: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 →
-                        ∀L2. L2 ⊑ L1 → L2 ⊢ T1 ⬌* T2.
-#L1 #T1 #T2 #HT12
+lemma lsubr_cpcs_trans: ∀G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬌* T2 →
+                        ∀L2. L2 ⊑ L1 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
+#G #L1 #T1 #T2 #HT12
 elim (cpcs_inv_cprs … HT12) -HT12
 /3 width=5 by cprs_div, lsubr_cprs_trans/ (**) (* /3 width=5/ is a bit slow *)
 qed-.
 
 (* Basic_1: was: pc3_lift *)
-lemma cpcs_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+lemma cpcs_lift: ∀G,L,K,d,e. ⇩[d, e] L ≡ K →
                  ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 →
-                 K ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
-#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
+                 ⦃G, K⦄ ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
+#G #L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
 elim (lift_total T d e) #U #HTU
 lapply (cprs_lift … HT1 … HLK … HTU1 … HTU) -T1 #HU1
 lapply (cprs_lift … HT2 … HLK … HTU2 … HTU) -K -T2 -T -d -e /2 width=3/
 qed.
 
-lemma cpcs_strip: ∀L,T1,T. ⦃G, L⦄ ⊢ T ⬌* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌ T2 →
+lemma cpcs_strip: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ⬌* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌ T2 →
                   ∃∃T0. ⦃G, L⦄ ⊢ T1 ⬌ T0 & ⦃G, L⦄ ⊢ T2 ⬌* T0.
-#L #T1 #T @TC_strip1 /2 width=3/ qed-.
+#G #L #T1 #T @TC_strip1 /2 width=3 by cpc_conf/ qed-.
 
 (* More inversion lemmas ****************************************************)
 
-lemma cpcs_inv_abst_sn: ∀a1,a2,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 →
-                        ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & L.ⓛW1 ⊢ T1 ⬌* T2 & a1 = a2.
-#a1 #a2 #L #W1 #W2 #T1 #T2 #H
+lemma cpcs_inv_abst_sn: ∀a1,a2,G,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 →
+                        ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬌* T2 & a1 = a2.
+#a1 #a2 #G #L #W1 #W2 #T1 #T2 #H
 elim (cpcs_inv_cprs … H) -H #T #H1 #H2
 elim (cprs_inv_abst1 … H1) -H1 #W0 #T0 #HW10 #HT10 #H destruct
 elim (cprs_inv_abst1 … H2) -H2 #W #T #HW2 #HT2 #H destruct
@@ -175,9 +180,9 @@ lapply (lprs_cpcs_trans … (L.ⓛW1) … HT2) /2 width=1/ -HT2 #HT2
 /4 width=3 by and3_intro, cprs_div, cpcs_cprs_div, cpcs_sym/
 qed-.
 
-lemma cpcs_inv_abst_dx: ∀a1,a2,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 →
-                        ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & L. ⓛW2 ⊢ T1 ⬌* T2 & a1 = a2.
-#a1 #a2 #L #W1 #W2 #T1 #T2 #HT12
+lemma cpcs_inv_abst_dx: ∀a1,a2,G,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 →
+                        ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & ⦃G, L.ⓛW2⦄ ⊢ T1 ⬌* T2 & a1 = a2.
+#a1 #a2 #G #L #W1 #W2 #T1 #T2 #HT12
 lapply (cpcs_sym … HT12) -HT12 #HT12
 elim (cpcs_inv_abst_sn … HT12) -HT12 /3 width=1/
 qed-.
@@ -185,29 +190,32 @@ qed-.
 (* Main properties **********************************************************)
 
 (* Basic_1: was pc3_t *)
-theorem cpcs_trans: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 @(trans_TC … HT1) qed-.
+theorem cpcs_trans: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #HT1 #T2 @(trans_TC … HT1) qed-.
 
-theorem cpcs_canc_sn: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T ⬌* T1 → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+theorem cpcs_canc_sn: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T ⬌* T1 → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3 by cpcs_trans, cpcs_sym/ qed-. (**) (* /3 width=3/ is too slow *)
 
-theorem cpcs_canc_dx: ∀L,T,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T2 ⬌* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+theorem cpcs_canc_dx: ∀G,L,T,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T2 ⬌* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3 by cpcs_trans, cpcs_sym/ qed-. (**) (* /3 width=3/ is too slow *)
 
-lemma cpcs_bind1: ∀a,I,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. L.ⓑ{I}V1 ⊢ T1 ⬌* T2 →
+lemma cpcs_bind1: ∀a,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 →
+                  ∀T1,T2. ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ⬌* T2 →
                   ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T1 ⬌* ⓑ{a,I}V2. T2.
-#a #I #L #V1 #V2 #HV12 #T1 #T2 #HT12
+#a #I #G #L #V1 #V2 #HV12 #T1 #T2 #HT12
 @(cpcs_trans … (ⓑ{a,I}V1.T2)) /2 width=1/
 qed.
 
-lemma cpcs_bind2: ∀a,I,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ∀T1,T2. L.ⓑ{I}V2 ⊢ T1 ⬌* T2 →
+lemma cpcs_bind2: ∀a,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬌* V2 →
+                  ∀T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬌* T2 →
                   ⦃G, L⦄ ⊢ ⓑ{a,I}V1. T1 ⬌* ⓑ{a,I}V2. T2.
-#a #I #L #V1 #V2 #HV12 #T1 #T2 #HT12
+#a #I #G #L #V1 #V2 #HV12 #T1 #T2 #HT12
 @(cpcs_trans … (ⓑ{a,I}V2.T1)) /2 width=1/
 qed.
 
 (* Basic_1: was: pc3_wcpr0 *)
-lemma lpr_cpcs_conf: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H
+lemma lpr_cpcs_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                     ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ⬌* T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
+#G #L1 #L2 #HL12 #T1 #T2 #H
 elim (cpcs_inv_cprs … H) -H /3 width=5 by cpcs_canc_dx, lpr_cprs_conf/
 qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
index 30ee9fb9d..69641dbf7 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
@@ -20,40 +20,40 @@ include "basic_2/equivalence/cpcs.ma".
 (* Properties about context sensitive computation on terms ******************)
 
 (* Basic_1: was: pc3_pr3_r *)
-lemma cpcs_cprs_dx: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /3 width=3/
+lemma cpcs_cprs_dx: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /3 width=3/
 qed.
 
 (* Basic_1: was: pc3_pr3_x *)
-lemma cpcs_cprs_sn: ∀L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /3 width=3/
+lemma cpcs_cprs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /3 width=3/
 qed.
 
-lemma cpcs_cprs_strap1: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /2 width=3/
+lemma cpcs_cprs_strap1: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /2 width=3/
 qed.
 
-lemma cpcs_cprs_strap2: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /width=1/ /2 width=3/
+lemma cpcs_cprs_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /width=1/ /2 width=3/
 qed.
 
-lemma cpcs_cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /2 width=3/
+lemma cpcs_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /2 width=3/
 qed.
 
 (* Basic_1: was: pc3_pr3_conf *)
-lemma cpcs_cprs_conf: ∀L,T1,T. ⦃G, L⦄ ⊢ T ➡* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /width=1/ /2 width=3/
+lemma cpcs_cprs_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /width=1/ /2 width=3/
 qed.
 
 (* Basic_1: was: pc3_pr3_t *)
 (* Basic_1: note: pc3_pr3_t should be renamed *)
-lemma cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=1/ /2 width=3/
+lemma cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=1/ /2 width=3/
 qed.
 
-lemma cprs_cpr_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cprs_cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=5 by cpr_cprs, cprs_div/ qed-.
 
-lemma cpr_cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpr_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3 by cpr_cprs, cprs_div/ qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_3.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_4.ma
similarity index 89%
rename from matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_3.ma
rename to matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_4.ma
index c4a789ab8..a7563d0c0 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_3.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconv_4.ma
@@ -14,6 +14,6 @@
 
 (* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
 
-notation "hvbox( ⦃G, L⦄ ⊢ break term 46 T1 ⬌ break term 46 T2 )"
+notation "hvbox( ⦃ term 46 G, break term 46 L ⦄ ⊢ break term 46 T1 ⬌ break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'PConv $L $T1 $T2 }.
+   for @{ 'PConv $G $L $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_3.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_4.ma
similarity index 89%
rename from matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_3.ma
rename to matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_4.ma
index 2088bc68d..f263e5d06 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_3.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconvstar_4.ma
@@ -14,6 +14,6 @@
 
 (* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
 
-notation "hvbox( ⦃G, L⦄ ⊢ break term 46 T1 ⬌* break term 46 T2 )"
+notation "hvbox( ⦃ term 46 G, break term 46 L ⦄ ⊢ break term 46 T1 ⬌* break term 46 T2 )"
    non associative with precedence 45
-   for @{ 'PConvStar $L $T1 $T2 }.
+   for @{ 'PConvStar $G $L $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 7a7d92d17..0bd584cac 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -40,19 +40,19 @@ table {
         ]
 *)
         [ { "\"big tree\" parallel computation" * } {
-             [ "yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )" "yprs_yprs"  "ygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )" "ygt_ygt" * ]
+             [ "yprs ( ? ⊢ ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "yprs_yprs"  "ygt ( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "ygt_ygt" * ]
           }
         ]
         [ { "\"big tree\" parallel reduction" * } {
-             [ "ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )" "ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )" * ]
+             [ "ypr ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "ysc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" * ]
           }
         ]
         [ { "local env. ref. for stratified native validity" * } {
-             [ "lsubsv ( ? ⊢ ? ¡⊑[?] ? )" "lsubsv_ldrop" + "lsubsv_lsuba" + "lsubsv_ssta" + "lsubsv_dxprs" + "lsubsv_cpcs" + "lsubsv_snv" * ]
+             [ "lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsuba" + "lsubsv_ssta" + "lsubsv_dxprs" + "lsubsv_cpcs" + "lsubsv_snv" * ]
           }
         ]
         [ { "stratified native validity" * } {
-             [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?] )" "snv_lift" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_lpr" + "snv_lpr" + "snv_cpcs" * ]
+             [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_lpr" + "snv_lpr" + "snv_cpcs" * ]
           }
         ]
      }
@@ -60,7 +60,7 @@ table {
    class "blue"
    [ { "equivalence" * } {
         [ { "context-sensitive equivalence" * } {
-             [ "cpcs ( ? ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
+             [ "cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
           }
         ]
      }
@@ -68,7 +68,7 @@ table {
    class "sky"
    [ { "conversion" * } {
         [ { "context-sensitive conversion" * } {
-             [ "cpc ( ? ⊢ ? ⬌ ? )" "cpc_cpc" * ]
+             [ "cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )" "cpc_cpc" * ]
           }
         ]
      }
-- 
2.39.5