From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sun, 17 Mar 2013 23:31:36 +0000 (+0000)
Subject: sfr renamed as lbotr and its symbol changed according to lsubr
X-Git-Tag: make_still_working~1209
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=6ac78e984f3ddee01251ef0ce13a692f062d7d5f;p=helm.git

sfr renamed as lbotr and its symbol changed according to lsubr
---

diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation.ma b/matita/matita/contribs/lambdadelta/basic_2/notation.ma
index de8221468..4aa5cd88a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/notation.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/notation.ma
@@ -146,13 +146,13 @@ notation "hvbox( ⇧ [ term 46 d , break term 46 e ] break term 46 T1 ≡ break
    non associative with precedence 45
    for @{ 'RLift $d $e $T1 $T2 }.
 
-notation "hvbox( T1 break ⊑ [ term 46 d , break term 46 e ] break term 46 T2 )"
+notation "hvbox( L1 break ⊑ [ term 46 d , break term 46 e ] break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'SubEq $T1 $d $e $T2 }.
+   for @{ 'SubEq $L1 $d $e $L2 }.
 
-notation "hvbox( ≽ [ term 46 d , break term 46 e ] break term 46 T2 )"
+notation "hvbox( ⊒ [ term 46 d , break term 46 e ] break term 46 L2 )"
    non associative with precedence 45
-   for @{ 'SubEqBottom $d $e $T2 }.
+   for @{ 'SubEqBottom $d $e $L2 }.
 
 notation "hvbox( ⇩ [ term 46 e ] break term 46 L1 ≡ break term 46 L2 )"
    non associative with precedence 45
diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_lbotr.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_lbotr.ma
new file mode 100644
index 000000000..1ff849657
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_lbotr.ma
@@ -0,0 +1,94 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/substitution/lsubr_lbotr.ma".
+include "basic_2/substitution/ldrop_ldrop.ma".
+
+(* DROPPING *****************************************************************)
+
+(* Inversion lemmas about local env. full refinement for substitution *******)
+
+(* Note: ldrop_ldrop not needed *)
+lemma lbotr_inv_ldrop: ∀I,L,K,V,i. ⇩[0, i] L ≡ K. ⓑ{I}V → ∀d,e. ⊒[d, e] L →
+                       d ≤ i → i < d + e → I = Abbr.
+#I #L elim L -L
+[ #K #V #i #H
+  lapply (ldrop_inv_atom1 … H) -H #H destruct
+| #L #J #W #IHL #K #V #i #H
+  elim (ldrop_inv_O1 … H) -H *
+  [ -IHL #H1 #H2 #d #e #HL #Hdi #Hide destruct
+    lapply (le_n_O_to_eq … Hdi) -Hdi #H destruct
+    lapply (HL … (L.ⓓW) ?) -HL /2 width=1/ #H
+    elim (lsubr_inv_abbr2 … H ?) -H // -Hide #K #_ #H destruct //
+  | #Hi #HLK #d @(nat_ind_plus … d) -d
+    [ #e #H #_ #Hide
+      elim (lbotr_inv_bind … H ?) -H [2: /2 width=2/ ] #HL #H destruct
+      @(IHL … HLK … HL) -IHL -HLK -HL // /2 width=1/
+    | #d #_ #e #H #Hdi #Hide
+      lapply (lbotr_inv_skip … H ?) -H // #HL
+      @(IHL … HLK … HL) -IHL -HLK -HL /2 width=1/
+    ]
+  ]
+]
+qed-.
+
+(* Properties about local env. full refinement for substitution *************)
+
+(* Note: ldrop_ldrop not needed *)
+lemma lbotr_ldrop: ∀L,d,e.
+                   (∀I,K,V,i. d ≤ i → i < d + e → ⇩[0, i] L ≡ K. ⓑ{I}V → I = Abbr) →
+                   ⊒[d, e] L.
+#L elim L -L //
+#L #I #V #IHL #d @(nat_ind_plus … d) -d
+[ #e @(nat_ind_plus … e) -e //
+  #e #_ #H0
+  >(H0 I L V 0 ? ? ?) //
+  /5 width=6 by lbotr_abbr, ldrop_ldrop, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
+| #d #_ #e #H0
+  /5 width=6 by lbotr_skip, ldrop_ldrop, le_S_S, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
+]
+qed.
+
+lemma lbotr_ldrop_trans_le: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ∀dd,ee. ⊒[dd, ee] L1 →
+                            dd + ee ≤ d → ⊒[dd, ee] L2.
+#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hddee
+@lbotr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
+lapply (lt_to_le_to_lt … Hiddee Hddee) -Hddee #Hid
+elim (ldrop_trans_le … HL12 … HLK2 ?) -L2 /2 width=2/ #X #HLK1 #H
+elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #K1 #V1 #HK12 #HV21 #H destruct
+@(lbotr_inv_ldrop … HLK1 … HL1) -L1 -K1 -V1 //
+qed.
+
+lemma lbotr_ldrop_trans_be_up: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 →
+                               ∀dd,ee. ⊒[dd, ee] L1 →
+                               dd ≤ d + e → d + e ≤ dd + ee →
+                               ⊒[d, dd + ee - d - e] L2.
+#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hdde #Hddee
+@lbotr_ldrop #I #K2 #V2 #i #Hdi #Hiddee #HLK2
+lapply (transitive_le ? ? (i+e)… Hdde ?) -Hdde /2 width=1/ #Hddie
+>commutative_plus in Hiddee; >minus_minus_comm <plus_minus_m_m /2 width=1/ -Hddee #Hiddee
+lapply (ldrop_trans_ge … HL12 … HLK2 ?) -L2 // -Hdi  #HL1K2
+@(lbotr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus // -Hddie /2 width=1/
+qed.
+
+lemma lbotr_ldrop_trans_ge: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ∀dd,ee. ⊒[dd, ee] L1 →
+                            d + e ≤ dd → ⊒[dd - e, ee] L2.
+#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hddee
+@lbotr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
+elim (le_inv_plus_l … Hddee) -Hddee #Hdde #Hedd
+>plus_minus in Hiddee; // #Hiddee
+lapply (transitive_le … Hdde Hddi) -Hdde #Hid
+lapply (ldrop_trans_ge … HL12 … HLK2 ?) -L2 // -Hid #HL1K2
+@(lbotr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus /2 width=1/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma
deleted file mode 100644
index 9d4cc3108..000000000
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma
+++ /dev/null
@@ -1,94 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/substitution/lsubr_sfr.ma".
-include "basic_2/substitution/ldrop_ldrop.ma".
-
-(* DROPPING *****************************************************************)
-
-(* Inversion lemmas about local env. full refinement for substitution *******)
-
-(* Note: ldrop_ldrop not needed *)
-lemma sfr_inv_ldrop: ∀I,L,K,V,i. ⇩[0, i] L ≡ K. ⓑ{I}V → ∀d,e. ≽ [d, e] L →
-                     d ≤ i → i < d + e → I = Abbr.
-#I #L elim L -L
-[ #K #V #i #H
-  lapply (ldrop_inv_atom1 … H) -H #H destruct
-| #L #J #W #IHL #K #V #i #H
-  elim (ldrop_inv_O1 … H) -H *
-  [ -IHL #H1 #H2 #d #e #HL #Hdi #Hide destruct
-    lapply (le_n_O_to_eq … Hdi) -Hdi #H destruct
-    lapply (HL … (L.ⓓW) ?) -HL /2 width=1/ #H
-    elim (lsubr_inv_abbr2 … H ?) -H // -Hide #K #_ #H destruct //
-  | #Hi #HLK #d @(nat_ind_plus … d) -d
-    [ #e #H #_ #Hide
-      elim (sfr_inv_bind … H ?) -H [2: /2 width=2/ ] #HL #H destruct
-      @(IHL … HLK … HL) -IHL -HLK -HL // /2 width=1/
-    | #d #_ #e #H #Hdi #Hide
-      lapply (sfr_inv_skip … H ?) -H // #HL
-      @(IHL … HLK … HL) -IHL -HLK -HL /2 width=1/
-    ]
-  ]
-]
-qed-.
-
-(* Properties about local env. full refinement for substitution *************)
-
-(* Note: ldrop_ldrop not needed *)
-lemma sfr_ldrop: ∀L,d,e.
-                 (∀I,K,V,i. d ≤ i → i < d + e → ⇩[0, i] L ≡ K. ⓑ{I}V → I = Abbr) →
-                 ≽ [d, e] L.
-#L elim L -L //
-#L #I #V #IHL #d @(nat_ind_plus … d) -d
-[ #e @(nat_ind_plus … e) -e //
-  #e #_ #H0
-  >(H0 I L V 0 ? ? ?) //
-  /5 width=6 by sfr_abbr, ldrop_ldrop, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
-| #d #_ #e #H0
-  /5 width=6 by sfr_skip, ldrop_ldrop, le_S_S, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
-]
-qed.
-
-lemma sfr_ldrop_trans_le: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ∀dd,ee. ≽ [dd, ee] L1 →
-                          dd + ee ≤ d → ≽ [dd, ee] L2.
-#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hddee
-@sfr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
-lapply (lt_to_le_to_lt … Hiddee Hddee) -Hddee #Hid
-elim (ldrop_trans_le … HL12 … HLK2 ?) -L2 /2 width=2/ #X #HLK1 #H
-elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #K1 #V1 #HK12 #HV21 #H destruct
-@(sfr_inv_ldrop … HLK1 … HL1) -L1 -K1 -V1 //
-qed.
-
-lemma sfr_ldrop_trans_be_up: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 →
-                             ∀dd,ee. ≽ [dd, ee] L1 →
-                             dd ≤ d + e → d + e ≤ dd + ee →
-                             ≽ [d, dd + ee - d - e] L2.
-#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hdde #Hddee
-@sfr_ldrop #I #K2 #V2 #i #Hdi #Hiddee #HLK2
-lapply (transitive_le ? ? (i+e)… Hdde ?) -Hdde /2 width=1/ #Hddie
->commutative_plus in Hiddee; >minus_minus_comm <plus_minus_m_m /2 width=1/ -Hddee #Hiddee
-lapply (ldrop_trans_ge … HL12 … HLK2 ?) -L2 // -Hdi  #HL1K2
-@(sfr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus // -Hddie /2 width=1/
-qed.
-
-lemma sfr_ldrop_trans_ge: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → ∀dd,ee. ≽ [dd, ee] L1 →
-                          d + e ≤ dd → ≽ [dd - e, ee] L2.
-#L1 #L2 #d #e #HL12 #dd #ee #HL1 #Hddee
-@sfr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
-elim (le_inv_plus_l … Hddee) -Hddee #Hdde #Hedd
->plus_minus in Hiddee; // #Hiddee
-lapply (transitive_le … Hdde Hddi) -Hdde #Hid
-lapply (ldrop_trans_ge … HL12 … HLK2 ?) -L2 // -Hid #HL1K2
-@(sfr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus /2 width=1/
-qed.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_lbotr.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_lbotr.ma
new file mode 100644
index 000000000..92593a2ad
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_lbotr.ma
@@ -0,0 +1,73 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/substitution/lsubr.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR SUBSTITUTION ****************************)
+
+(* bottom element of the refinement *)
+definition lbotr: nat → nat → predicate lenv ≝
+   λd,e. NF_sn … (lsubr d e) (lsubr d e …).
+
+interpretation
+   "local environment full refinement (substitution)"
+   'SubEqBottom d e L = (lbotr d e L).
+
+(* Basic properties *********************************************************)
+
+lemma lbotr_atom: ∀d,e. ⊒[d, e] ⋆.
+#d #e #L #H
+elim (lsubr_inv_atom2 … H) -H
+[ #H destruct //
+| * #H1 #H2 destruct //
+]
+qed.
+
+lemma lbotr_OO: ∀L. ⊒[0, 0] L.
+// qed.
+
+lemma lbotr_abbr: ∀L,V,e. ⊒[0, e] L → ⊒[0, e + 1] L.ⓓV.
+#L #V #e #HL #K #H
+elim (lsubr_inv_abbr2 … H ?) -H // <minus_plus_m_m #X #HLX #H destruct
+lapply (HL … HLX) -HL -HLX /2 width=1/
+qed.
+
+lemma lbotr_abbr_O: ∀L,V. ⊒[0,1] L.ⓓV.
+#L #V
+@(lbotr_abbr … 0) //
+qed.
+
+lemma lbotr_skip: ∀I,L,V,d,e. ⊒[d, e] L → ⊒[d + 1, e] L.ⓑ{I}V.
+#I #L #V #d #e #HL #K #H
+elim (lsubr_inv_skip2 … H ?) -H // <minus_plus_m_m #J #X #W #HLX #H destruct
+lapply (HL … HLX) -HL -HLX /2 width=1/
+qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma lbotr_inv_bind: ∀I,L,V,e. ⊒[0, e] L.ⓑ{I}V → 0 < e →
+                      ⊒[0, e - 1] L ∧ I = Abbr.
+#I #L #V #e #HL #He
+lapply (HL (L.ⓓV) ?) /2 width=1/ #H
+elim (lsubr_inv_abbr2 … H ?) -H // #K #_ #H destruct
+@conj // #L #HKL
+lapply (HL (L.ⓓV) ?) -HL /2 width=1/ -HKL #H
+elim (lsubr_inv_abbr2 … H ?) -H // -He #X #HLX #H destruct //
+qed-.
+
+lemma lbotr_inv_skip: ∀I,L,V,d,e. ⊒[d, e] L.ⓑ{I}V → 0 < d → ⊒[d - 1, e] L.
+#I #L #V #d #e #HL #Hd #K #HLK
+lapply (HL (K.ⓑ{I}V) ?) -HL /2 width=1/ -HLK #H
+elim (lsubr_inv_skip2 … H ?) -H // -Hd #J #X #W #HKX #H destruct //
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_sfr.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_sfr.ma
deleted file mode 100644
index e35a371bc..000000000
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_sfr.ma
+++ /dev/null
@@ -1,73 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/substitution/lsubr.ma".
-
-(* LOCAL ENVIRONMENT REFINEMENT FOR SUBSTITUTION ****************************)
-
-(* bottom element of the refinement *)
-definition sfr: nat → nat → predicate lenv ≝
-   λd,e. NF_sn … (lsubr d e) (lsubr d e …).
-
-interpretation
-   "local environment full refinement (substitution)"
-   'SubEqBottom d e L = (sfr d e L).
-
-(* Basic properties *********************************************************)
-
-lemma sfr_atom: ∀d,e. ≽ [d, e] ⋆.
-#d #e #L #H
-elim (lsubr_inv_atom2 … H) -H
-[ #H destruct //
-| * #H1 #H2 destruct //
-]
-qed.
-
-lemma sfr_OO: ∀L. ≽ [0, 0] L.
-// qed.
-
-lemma sfr_abbr: ∀L,V,e. ≽ [0, e] L → ≽ [0, e + 1] L.ⓓV.
-#L #V #e #HL #K #H
-elim (lsubr_inv_abbr2 … H ?) -H // <minus_plus_m_m #X #HLX #H destruct
-lapply (HL … HLX) -HL -HLX /2 width=1/
-qed.
-
-lemma sfr_abbr_O: ∀L,V. ≽[0,1] L.ⓓV.
-#L #V
-@(sfr_abbr … 0) //
-qed.
-
-lemma sfr_skip: ∀I,L,V,d,e. ≽ [d, e] L → ≽ [d + 1, e] L.ⓑ{I}V.
-#I #L #V #d #e #HL #K #H
-elim (lsubr_inv_skip2 … H ?) -H // <minus_plus_m_m #J #X #W #HLX #H destruct
-lapply (HL … HLX) -HL -HLX /2 width=1/
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma sfr_inv_bind: ∀I,L,V,e. ≽ [0, e] L.ⓑ{I}V → 0 < e →
-                    ≽ [0, e - 1] L ∧ I = Abbr.
-#I #L #V #e #HL #He
-lapply (HL (L.ⓓV) ?) /2 width=1/ #H
-elim (lsubr_inv_abbr2 … H ?) -H // #K #_ #H destruct
-@conj // #L #HKL
-lapply (HL (L.ⓓV) ?) -HL /2 width=1/ -HKL #H
-elim (lsubr_inv_abbr2 … H ?) -H // -He #X #HLX #H destruct //
-qed-.
-
-lemma sfr_inv_skip: ∀I,L,V,d,e. ≽ [d, e] L.ⓑ{I}V → 0 < d → ≽ [d - 1, e] L.
-#I #L #V #d #e #HL #Hd #K #HLK
-lapply (HL (K.ⓑ{I}V) ?) -HL /2 width=1/ -HLK #H
-elim (lsubr_inv_skip2 … H ?) -H // -Hd #J #X #W #HKX #H destruct //
-qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/delift_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/delift_lift.ma
index eb3dc1f28..8abaeb9f9 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/delift_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/delift_lift.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/ldrop_sfr.ma".
+include "basic_2/substitution/ldrop_lbotr.ma".
 include "basic_2/unfold/tpss_lift.ma".
 include "basic_2/unfold/delift.ma".
 
@@ -30,8 +30,8 @@ lapply (lift_conf_be … HVU2 … HV2U ?) //
 >commutative_plus in ⊢ (??%??→?); <minus_plus_m_m /3 width=6/
 qed.
 
-lemma sfr_delift: ∀L,T1,d,e. d + e ≤ |L| → ≽ [d, e] L →
-                  ∃T2. L ⊢ ▼*[d, e] T1 ≡ T2.
+lemma lbotr_delift: ∀L,T1,d,e. d + e ≤ |L| → ⊒[d, e] L →
+                    ∃T2. L ⊢ ▼*[d, e] T1 ≡ T2.
 #L #T1 @(f2_ind … fw … L T1) -L -T1
 #n #IH #L * * /2 width=2/
 [ #i #H #d #e #Hde #HL destruct
@@ -39,11 +39,11 @@ lemma sfr_delift: ∀L,T1,d,e. d + e ≤ |L| → ≽ [d, e] L →
   elim (lt_or_ge i (d+e)) #Hide [2: /3 width=2/ ]
   lapply (lt_to_le_to_lt … Hide Hde) #Hi
   elim (ldrop_O1_lt … Hi) -Hi #I #K #V1 #HLK
-  lapply (sfr_inv_ldrop … HLK … HL ? ?) // #H destruct
+  lapply (lbotr_inv_ldrop … HLK … HL ? ?) // #H destruct
   lapply (ldrop_pair2_fwd_fw … HLK (#i)) #HKL
   lapply (ldrop_fwd_ldrop2 … HLK) #HLK0
   lapply (ldrop_fwd_O1_length … HLK0) #H
-  lapply (sfr_ldrop_trans_be_up … HLK0 … HL ? ?) -HLK0 -HL
+  lapply (lbotr_ldrop_trans_be_up … HLK0 … HL ? ?) -HLK0 -HL
   [1,2: /2 width=1/ | <minus_n_O <minus_plus ] #HK
   elim (IH … HKL … HK) -IH -HKL -HK
   [2: >H -H /2 width=1/ ] -Hde -H #V2 #V12 (**) (* H erased two times *)
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 7ebbbca7f..2b88582a7 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
@@ -235,11 +235,11 @@ table {
           }
         ]
         [ { "basic local env. slicing" * } {
-             [ "ldrop ( ⇩[?,?] ? ≡ ? )" "ldrop_append" + "ldrop_lpx" + "ldrop_sfr" + "ldrop_ldrop" * ]
+             [ "ldrop ( ⇩[?,?] ? ≡ ? )" "ldrop_append" + "ldrop_lpx" + "ldrop_lbotr" + "ldrop_ldrop" * ]
           }
         ]
         [ { "local env. ref. for substitution" * } {
-             [ "lsubr ( ? ⊑[?,?] ? )" "(lsubr_lsubr)" "lsubr_sfr ( ≽[?,?] ? )" * ]
+             [ "lsubr ( ? ⊑[?,?] ? )" "(lsubr_lsubr)" "lsubr_lbotr ( ⊒[?,?] ? )" * ]
           }
         ]
         [ { "restricted structural predecessor for closures" * } {