From 6ac78e984f3ddee01251ef0ce13a692f062d7d5f Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sun, 17 Mar 2013 23:31:36 +0000
Subject: [PATCH] sfr renamed as lbotr and its symbol changed according to
 lsubr

---
 .../contribs/lambdadelta/basic_2/notation.ma  |  8 ++--
 .../{ldrop_sfr.ma => ldrop_lbotr.ma}          | 48 +++++++++----------
 .../{lsubr_sfr.ma => lsubr_lbotr.ma}          | 22 ++++-----
 .../lambdadelta/basic_2/unfold/delift_lift.ma | 10 ++--
 .../lambdadelta/basic_2/web/basic_2_src.tbl   |  4 +-
 5 files changed, 46 insertions(+), 46 deletions(-)
 rename matita/matita/contribs/lambdadelta/basic_2/substitution/{ldrop_sfr.ma => ldrop_lbotr.ma} (63%)
 rename matita/matita/contribs/lambdadelta/basic_2/substitution/{lsubr_sfr.ma => lsubr_lbotr.ma} (79%)

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_sfr.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_lbotr.ma
similarity index 63%
rename from matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma
rename to matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_lbotr.ma
index 9d4cc3108..1ff849657 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_sfr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrop_lbotr.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/lsubr_sfr.ma".
+include "basic_2/substitution/lsubr_lbotr.ma".
 include "basic_2/substitution/ldrop_ldrop.ma".
 
 (* DROPPING *****************************************************************)
@@ -20,8 +20,8 @@ include "basic_2/substitution/ldrop_ldrop.ma".
 (* 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.
+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
@@ -33,10 +33,10 @@ lemma sfr_inv_ldrop: ∀I,L,K,V,i. ⇩[0, i] L ≡ K. ⓑ{I}V → ∀d,e. ≽ [d
     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
+      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 (sfr_inv_skip … H ?) -H // #HL
+      lapply (lbotr_inv_skip … H ?) -H // #HL
       @(IHL … HLK … HL) -IHL -HLK -HL /2 width=1/
     ]
   ]
@@ -46,49 +46,49 @@ 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.
+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 sfr_abbr, ldrop_ldrop, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
+  /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 sfr_skip, ldrop_ldrop, le_S_S, lt_minus_to_plus_r/ (**) (* auto now too slow without trace *)
+  /5 width=6 by lbotr_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.
+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
-@sfr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
+@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
-@(sfr_inv_ldrop … HLK1 … HL1) -L1 -K1 -V1 //
+@(lbotr_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.
+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
-@sfr_ldrop #I #K2 #V2 #i #Hdi #Hiddee #HLK2
+@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
-@(sfr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus // -Hddie /2 width=1/
+@(lbotr_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.
+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
-@sfr_ldrop #I #K2 #V2 #i #Hddi #Hiddee #HLK2
+@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
-@(sfr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus /2 width=1/
+@(lbotr_inv_ldrop … HL1K2 … HL1) -L1 >commutative_plus /2 width=1/
 qed.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_sfr.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_lbotr.ma
similarity index 79%
rename from matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_sfr.ma
rename to matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_lbotr.ma
index e35a371bc..92593a2ad 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_sfr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lsubr_lbotr.ma
@@ -17,16 +17,16 @@ include "basic_2/substitution/lsubr.ma".
 (* LOCAL ENVIRONMENT REFINEMENT FOR SUBSTITUTION ****************************)
 
 (* bottom element of the refinement *)
-definition sfr: nat → nat → predicate lenv ≝
+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 = (sfr d e L).
+   'SubEqBottom d e L = (lbotr d e L).
 
 (* Basic properties *********************************************************)
 
-lemma sfr_atom: ∀d,e. ≽ [d, e] ⋆.
+lemma lbotr_atom: ∀d,e. ⊒[d, e] ⋆.
 #d #e #L #H
 elim (lsubr_inv_atom2 … H) -H
 [ #H destruct //
@@ -34,21 +34,21 @@ elim (lsubr_inv_atom2 … H) -H
 ]
 qed.
 
-lemma sfr_OO: ∀L. ≽ [0, 0] L.
+lemma lbotr_OO: ∀L. ⊒[0, 0] L.
 // qed.
 
-lemma sfr_abbr: ∀L,V,e. ≽ [0, e] L → ≽ [0, e + 1] L.ⓓV.
+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 sfr_abbr_O: ∀L,V. ≽[0,1] L.ⓓV.
+lemma lbotr_abbr_O: ∀L,V. ⊒[0,1] L.ⓓV.
 #L #V
-@(sfr_abbr … 0) //
+@(lbotr_abbr … 0) //
 qed.
 
-lemma sfr_skip: ∀I,L,V,d,e. ≽ [d, e] L → ≽ [d + 1, e] L.ⓑ{I}V.
+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/
@@ -56,8 +56,8 @@ 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.
+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
@@ -66,7 +66,7 @@ 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.
+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 //
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" * } {
-- 
2.39.2