update in delayed_updating

+ balanced reduction with main theorem proved
+ notation change for lift

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr.etc
deleted file mode 100644 (file)
index f82db8a..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr.etc
+++ /dev/null
@@ -1,36 +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 "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/syntax/prototerm_constructors.ma".
-include "delayed_updating/syntax/prototerm_eq.ma".
-include "delayed_updating/syntax/path_closed.ma".
-include "delayed_updating/syntax/path_balanced.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
-include "ground/arith/nat_rplus.ma".
-include "ground/xoa/ex_6_5.ma".
-
-(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
-
-definition dbfr (r): relation2 prototerm prototerm ≝
-           λt1,t2.
-           ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
-           ⊗b ϵ 𝐁 & b ϵ 𝐂❨m❩ & q ϵ 𝐂❨n❩ & r◖𝗱↑n ϵ t1 &
-           t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
-.
-
-interpretation
-  "balanced focused reduction with delayed updating (prototerm)"
-  'BlackRightArrowDBF t1 r t2 = (dbfr r t1 t2).

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr_ibfr.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr_ibfr.etc
deleted file mode 100644 (file)
index d7c16ca..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr_ibfr.etc
+++ /dev/null
@@ -1,79 +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 "delayed_updating/reduction/dbfr.ma".
-include "delayed_updating/reduction/ibfr.ma".
-
-include "delayed_updating/unwind/unwind2_constructors.ma".
-include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
-include "delayed_updating/unwind/unwind2_preterm_eq.ma".
-include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
-include "delayed_updating/unwind/unwind2_rmap_closed.ma".
-
-include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
-
-include "delayed_updating/syntax/prototerm_proper_constructors.ma".
-include "delayed_updating/syntax/path_closed_structure.ma".
-include "delayed_updating/syntax/path_structure_depth.ma".
-
-(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
-
-(* Main destructions with ibfr **********************************************)
-
-theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
-        t1 ➡𝐝𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
-#f #t1 #t2 #r #H0t1
-* #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
-@(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
-[ -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 //
-| -H0t1 -Hm -Hn -Ht1 -Ht2 //
-| -H0t1 -Hb -Hn -Ht1 -Ht2
-  /2 width=2 by path_closed_structure_depth/
-| -H0t1 -Hb -Hm -Ht1 -Ht2
-  /2 width=2 by path_closed_structure_depth/
-| lapply (in_comp_unwind2_path_term f … Ht1) -H0t1 -Hb -Hm -Ht2 -Ht1
-  <unwind2_path_d_dx <tr_pap_succ_nap >list_append_rcons_dx >list_append_assoc
-  <unwind2_rmap_append_closed_nap //
-| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
-(*
-  lapply (path_head_refl_append_bi … Hh H1k) -Hh -H1k <nrplus_inj_sn #H1k
-*)
-  @(subset_eq_trans … Ht2) -t2
-  @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
-  [ @fsubst_eq_repl [ // | // ]
-    @(subset_eq_trans … (unwind2_term_iref …))
-    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
-    [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
-    @(subset_eq_trans … (lift_unwind2_term_after …))
-    @unwind2_term_eq_repl_sn
-(* Note: crux of the proof begins *)
-    <list_append_rcons_sn
-    @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
-    @tr_compose_eq_repl
-(* TODO  
-    [ <unwind2_rmap_append_closed_nap //   
-      <depth_append <depth_L_sn
-      <nplus_comm <nrplus_npsucc_sn <nplus_succ_sn //
-    | >unwind2_rmap_A_dx
-      /2 width=1 by tls_unwind2_rmap_closed/
-    ]
-*)
-(* Note: crux of the proof ends *)
-  | //
-  | /2 width=2 by ex_intro/
-  | //
-  ]
-]
-qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr_lift.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr_lift.etc
deleted file mode 100644 (file)
index f237289..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr_lift.etc
+++ /dev/null
@@ -1,51 +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 "delayed_updating/reduction/dbfr.ma".
-
-include "delayed_updating/substitution/fsubst_lift.ma".
-include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_constructors.ma".
-include "delayed_updating/substitution/lift_path_head.ma".
-include "delayed_updating/substitution/lift_rmap_head.ma".
-
-(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
-
-(* Constructions with lift **************************************************)
-
-theorem dfr_lift_bi (f) (t1) (t2) (r):
-        t1 ➡𝐝𝐛𝐟[r] t2 → ↑[f]t1 ➡𝐝𝐛𝐟[↑[f]r] ↑[f]t2.
-#f #t1 #t2 #r
-* #p #q #k #Hr #H1k #Ht1 #Ht2 destruct
-@(ex4_3_intro … (↑[f]p) (↑[↑[p◖𝗔◖𝗟]f]q) ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨k❩))
-[ -H1k -Ht1 -Ht2 //
-| -Ht1 -Ht2
-  <lift_rmap_L_dx >lift_path_L_sn
-  <(lift_path_head_closed … H1k) in ⊢ (??%?); -H1k //
-| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1k
-  <lift_path_d_dx #Ht1 //
-| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
-  @(subset_eq_trans … Ht2) -t2
-  @(subset_eq_trans … (lift_term_fsubst …))
-  @fsubst_eq_repl [ // | // ]
-  @(subset_eq_trans … (lift_term_iref …))
-  @iref_eq_repl
-  @(subset_eq_canc_sn … (lift_term_grafted_S …))
-  @lift_term_eq_repl_sn
-(* Note: crux of the proof begins *)
-  >list_append_rcons_sn in H1k; #H1k >lift_rmap_A_dx
-  /2 width=1 by tls_lift_rmap_closed/
-(* Note: crux of the proof ends *)
-]
-qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/ibfr.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/ibfr.etc
deleted file mode 100644 (file)
index dfa14ef..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/ibfr.etc
+++ /dev/null
@@ -1,37 +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 "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/substitution/lift_prototerm.ma".
-include "delayed_updating/syntax/prototerm_eq.ma".
-include "delayed_updating/syntax/path_closed.ma".
-include "delayed_updating/syntax/path_balanced.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/notation/relations/black_rightarrow_ibf_3.ma".
-include "ground/relocation/tr_uni.ma".
-include "ground/arith/nat_rplus.ma".
-include "ground/xoa/ex_6_5.ma".
-
-(* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
-
-definition ibfr (r): relation2 prototerm prototerm ≝
-           λt1,t2.
-           ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
-           ⊗b ϵ 𝐁 & b ϵ 𝐂❨m❩ & q ϵ 𝐂❨n❩ & r◖𝗱↑n ϵ t1 &
-           t1[⋔r←↑[𝐮❨↑(m+n)❩](t1⋔(p◖𝗦))] ⇔ t2
-.
-
-interpretation
-  "balanced focused reduction with immediate updating (prototerm)"
-  'BlackRightArrowIBF t1 r t2 = (ibfr r t1 t2).

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/righttrianglearrow_2.ma b/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/righttrianglearrow_2.ma
new file mode 100644 (file)
index 0000000..38019a9
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/righttrianglearrow_2.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR DELAYED UPDATING ********************************************)
+
+notation "hvbox( 🠢[ break term 46 t1 ] break term 70 t2  )"
+  non associative with precedence 70
+  for @{ 'RightTriangleArrow $t1 $t2 }.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/uparrow_2.ma b/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/uparrow_2.ma
deleted file mode 100644 (file)
index b3123df..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/uparrow_2.ma
+++ /dev/null
@@ -1,19 +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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR DELAYED UPDATING ********************************************)
-
-notation "hvbox( ↑[ break term 46 t1 ] break term 70 t2  )"
-  non associative with precedence 70
-  for @{ 'UpArrow $t1 $t2 }.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/uptrianglearrow_2.ma b/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/uptrianglearrow_2.ma
new file mode 100644 (file)
index 0000000..e77ff43
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/notation/functions/uptrianglearrow_2.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR DELAYED UPDATING ********************************************)
+
+notation "hvbox( 🠡[ break term 46 t1 ] break term 70 t2  )"
+  non associative with precedence 70
+  for @{ 'UpTriangleArrow $t1 $t2 }.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma
new file mode 100644 (file)
index 0000000..b9b7246
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+include "delayed_updating/syntax/prototerm_eq.ma".
+include "delayed_updating/syntax/path_closed.ma".
+include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
+include "ground/arith/nat_rplus.ma".
+include "ground/xoa/ex_6_5.ma".
+
+(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
+
+definition dbfr (r): relation2 prototerm prototerm ≝
+           λt1,t2.
+           ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
+           ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓣ,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
+           t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
+.
+
+interpretation
+  "balanced focused reduction with delayed updating (prototerm)"
+  'BlackRightArrowDBF t1 r t2 = (dbfr r t1 t2).

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma
new file mode 100644 (file)
index 0000000..fd62cdd
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma
@@ -0,0 +1,72 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "delayed_updating/reduction/dbfr.ma".
+include "delayed_updating/reduction/ibfr.ma".
+
+include "delayed_updating/unwind/unwind2_constructors.ma".
+include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
+include "delayed_updating/unwind/unwind2_preterm_eq.ma".
+include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
+include "delayed_updating/unwind/unwind2_rmap_closed.ma".
+
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
+
+include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+include "delayed_updating/syntax/path_closed_structure.ma".
+include "delayed_updating/syntax/path_structure_depth.ma".
+
+(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
+
+(* Main destructions with ibfr **********************************************)
+
+theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
+        t1 ➡𝐝𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #H0t1
+* #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
+[ -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hb -Hn -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| -H0t1 -Hb -Hm -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term f … Ht1) -H0t1 -Hb -Hm -Ht2 -Ht1
+  <unwind2_path_d_dx <tr_pap_succ_nap >list_append_rcons_dx >list_append_assoc
+  <unwind2_rmap_append_closed_Lq_dx_nap_depth //
+| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
+  @(subset_eq_trans … Ht2) -t2
+  @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
+  [ @fsubst_eq_repl [ // | // ]
+    @(subset_eq_trans … (unwind2_term_iref …))
+    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+    [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
+    @(subset_eq_trans … (lift_unwind2_term_after …))
+    @unwind2_term_eq_repl_sn
+(* Note: crux of the proof begins *)
+    <list_append_rcons_sn
+    @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
+    @tr_compose_eq_repl
+    [ <unwind2_rmap_append_closed_bLq_dx_nap_plus //
+    | >unwind2_rmap_A_dx
+      /2 width=2 by tls_succ_plus_unwind2_rmap_append_closed_bLq_dx/
+    ]
+(* Note: crux of the proof ends *)
+  | //
+  | /2 width=2 by ex_intro/
+  | //
+  ]
+]
+qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
index 28b21e5e0e4a10c90e2ab904f85cdded8bc089df..ed5778166badfc540f70ee0159523c4c3935b8e2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
@@ -12,24 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "delayed_updating/reduction/dfr.ma".
+
 include "delayed_updating/substitution/fsubst_lift.ma".
 include "delayed_updating/substitution/fsubst_eq.ma".
 include "delayed_updating/substitution/lift_constructors.ma".
 include "delayed_updating/substitution/lift_path_closed.ma".
 include "delayed_updating/substitution/lift_rmap_closed.ma".
 
-(**) (* reverse include *)
-include "delayed_updating/reduction/dfr.ma".
-
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
 (* Constructions with lift **************************************************)
 
 theorem dfr_lift_bi (f) (t1) (t2) (r):
-        t1 ➡𝐝𝐟[r] t2 → ↑[f]t1 ➡𝐝𝐟[↑[f]r] ↑[f]t2.
+        t1 ➡𝐝𝐟[r] t2 → 🠡[f]t1 ➡𝐝𝐟[🠡[f]r] 🠡[f]t2.
 #f #t1 #t2 #r
 * #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
-@(ex4_3_intro … (↑[f]p) (↑[↑[p◖𝗔◖𝗟]f]q) ((↑[p●𝗔◗𝗟◗q]f)＠§❨n❩))
+@(ex4_3_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔◖𝗟)]q) (🠢[f](p●𝗔◗𝗟◗q)＠§❨n❩))
 [ -Hn -Ht1 -Ht2 //
 | -Ht1 -Ht2
   /2 width=1 by lift_path_rmap_closed_L/

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.ma
new file mode 100644 (file)
index 0000000..869ad57
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.ma
@@ -0,0 +1,37 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/substitution/lift_prototerm.ma".
+include "delayed_updating/syntax/prototerm_eq.ma".
+include "delayed_updating/syntax/path_closed.ma".
+include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/notation/relations/black_rightarrow_ibf_3.ma".
+include "ground/relocation/tr_uni.ma".
+include "ground/arith/nat_rplus.ma".
+include "ground/xoa/ex_6_5.ma".
+
+(* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
+
+definition ibfr (r): relation2 prototerm prototerm ≝
+           λt1,t2.
+           ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
+           ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓣ,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
+           t1[⋔r←🠡[𝐮❨↑(m+n)❩](t1⋔(p◖𝗦))] ⇔ t2
+.
+
+interpretation
+  "balanced focused reduction with immediate updating (prototerm)"
+  'BlackRightArrowIBF t1 r t2 = (ibfr r t1 t2).

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index 9bc8d994dcb6a934baed8787f52173136b314eff..2a6553d9d0dd428614c7fdb648ad3e2eff9e8261 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -26,7 +26,7 @@ definition ifr (r): relation2 prototerm prototerm ≝
            λt1,t2.
            ∃∃p,q,n. p●𝗔◗𝗟◗q = r &
            q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
-           t1[⋔r←↑[𝐮❨↑n❩](t1⋔(p◖𝗦))] ⇔ t2
+           t1[⋔r←🠡[𝐮❨↑n❩](t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
index 365447714982e2b05ee86fd519681a77d29c11e2..35a00a3682458f55d2109805b88b744ed31ef8bf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
@@ -28,10 +28,10 @@ include "ground/relocation/tr_compose_eq.ma".
 (* Constructions with lift **************************************************)
 
 theorem ifr_lift_bi (f) (t1) (t2) (r):
-        t1 ➡𝐢𝐟[r] t2 → ↑[f]t1 ➡𝐢𝐟[↑[f]r] ↑[f]t2.
+        t1 ➡𝐢𝐟[r] t2 → 🠡[f]t1 ➡𝐢𝐟[🠡[f]r] 🠡[f]t2.
 #f #t1 #t2 #r
 * #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
-@(ex4_3_intro … (↑[f]p) (↑[↑[p◖𝗔◖𝗟]f]q) ((↑[p●𝗔◗𝗟◗q]f)＠§❨n❩))
+@(ex4_3_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔◖𝗟)]q) (🠢[f](p●𝗔◗𝗟◗q)＠§❨n❩))
 [ -Hn -Ht1 -Ht2 //
 | -Ht1 -Ht2
   /2 width=1 by lift_path_rmap_closed_L/

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
index 383bc24f9b28519f680b4ac530a2de2fe5af8717..ad0de7230e87c803d0aade06d7b13f53738f9ab3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
@@ -20,7 +20,7 @@ include "delayed_updating/substitution/lift_prototerm_eq.ma".
 (* Constructions with lift for preterm **************************************)
 
 lemma lift_term_fsubst_sn (f) (t) (u) (p):
-      (↑[f]t)[⋔(↑[f]p)←↑[↑[p]f]u] ⊆ ↑[f](t[⋔p←u]).
+      (🠡[f]t)[⋔(🠡[f]p)←🠡[🠢[f]p]u] ⊆ 🠡[f](t[⋔p←u]).
 #f #t #u #p #ql * *
 [ #rl * #r #Hr #H1 #H2 destruct
   >lift_path_append
@@ -32,7 +32,7 @@ lemma lift_term_fsubst_sn (f) (t) (u) (p):
 qed-.
 
 lemma lift_term_fsubst_dx (f) (t) (u) (p):
-      ↑[f](t[⋔p←u]) ⊆ (↑[f]t)[⋔(↑[f]p)←↑[↑[p]f]u].
+      🠡[f](t[⋔p←u]) ⊆ (🠡[f]t)[⋔(🠡[f]p)←🠡[🠢[f]p]u].
 #f #t #u #p #ql * #q * *
 [ #r #Hu #H1 #H2 destruct
   @or_introl @ex2_intro
@@ -47,5 +47,5 @@ lemma lift_term_fsubst_dx (f) (t) (u) (p):
 qed-.
 
 lemma lift_term_fsubst (f) (t) (u) (p):
-      (↑[f]t)[⋔(↑[f]p)←↑[↑[p]f]u] ⇔ ↑[f](t[⋔p←u]).
+      (🠡[f]t)[⋔(🠡[f]p)←🠡[🠢[f]p]u] ⇔ 🠡[f](t[⋔p←u]).
 /3 width=1 by lift_term_fsubst_sn, conj, lift_term_fsubst_dx/ qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
index f263e2d140464896573bd1fddc5ebceaa2e322db..56f7b178a5400eda07f3e99156ee475719629b46 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -20,14 +20,14 @@ include "ground/relocation/nap.ma".
 (* LIFT FOR PROTOTERM *******************************************************)
 
 lemma lift_term_iref_pap_sn (f) (t:prototerm) (k:pnat):
-      (𝛕f＠⧣❨k❩.↑[⇂*[k]f]t) ⊆ ↑[f](𝛕k.t).
+      (𝛕f＠⧣❨k❩.🠡[⇂*[k]f]t) ⊆ 🠡[f](𝛕k.t).
 #f #t #k #p * #q * #r #Hr #H1 #H2 destruct
 @(ex2_intro … (𝗱k◗𝗺◗r))
 /2 width=1 by in_comp_iref/
 qed-.
 
 lemma lift_term_iref_pap_dx (f) (t) (k:pnat):
-      ↑[f](𝛕k.t) ⊆ 𝛕f＠⧣❨k❩.↑[⇂*[k]f]t.
+      🠡[f](𝛕k.t) ⊆ 𝛕f＠⧣❨k❩.🠡[⇂*[k]f]t.
 #f #t #k #p * #q #Hq #H0 destruct
 elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
 <lift_path_d_sn <lift_path_m_sn
@@ -35,18 +35,18 @@ elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
 qed-.
 
 lemma lift_term_iref_pap (f) (t) (k:pnat):
-      (𝛕f＠⧣❨k❩.↑[⇂*[k]f]t) ⇔ ↑[f](𝛕k.t).
+      (𝛕f＠⧣❨k❩.🠡[⇂*[k]f]t) ⇔ 🠡[f](𝛕k.t).
 /3 width=1 by conj, lift_term_iref_pap_sn, lift_term_iref_pap_dx/
 qed.
 
 lemma lift_term_iref_nap (f) (t) (n):
-      (𝛕↑(f＠§❨n❩).↑[⇂*[↑n]f]t) ⇔ ↑[f](𝛕↑n.t).
+      (𝛕↑(f＠§❨n❩).🠡[⇂*[↑n]f]t) ⇔ 🠡[f](𝛕↑n.t).
 #f #t #n
 >tr_pap_succ_nap //
 qed.
 
 lemma lift_term_iref_uni (t) (n) (k):
-      (𝛕(k+n).t) ⇔ ↑[𝐮❨n❩](𝛕k.t).
+      (𝛕(k+n).t) ⇔ 🠡[𝐮❨n❩](𝛕k.t).
 #t #n #k
 @(subset_eq_trans … (lift_term_iref_pap …))
 <tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path.ma
index 2154e4a559e5c6d5f6e0a728318ea530fa83ac75..0887edfc873412bede700a4d2a1b5e25b054bbf8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path.ma
@@ -20,47 +20,47 @@ include "delayed_updating/substitution/lift_rmap.ma".
 rec definition lift_path (f) (p) on p: path ≝
 match p with
 [ list_empty     ⇒ (𝐞)
-| list_lcons l q ⇒ (lift_path f q)◖↑[↑[q]f]l
+| list_lcons l q ⇒ (lift_path f q)◖🠡[🠢[f]q]l
 ].
 
 interpretation
   "lift (path)"
-  'UpArrow f l = (lift_path f l).
+  'UpTriangleArrow f l = (lift_path f l).
 
 (* Basic constructions ******************************************************)
 
 lemma lift_path_empty (f):
-      (𝐞) = ↑[f]𝐞.
+      (𝐞) = 🠡[f]𝐞.
 // qed.
 
 lemma lift_path_rcons (f) (p) (l):
-      (↑[f]p)◖↑[↑[p]f]l = ↑[f](p◖l).
+      (🠡[f]p)◖🠡[🠢[f]p]l = 🠡[f](p◖l).
 // qed.
 
 lemma lift_path_d_dx (f) (p) (k):
-      (↑[f]p)◖𝗱((↑[p]f)＠⧣❨k❩) = ↑[f](p◖𝗱k).
+      (🠡[f]p)◖𝗱(🠢[f]p＠⧣❨k❩) = 🠡[f](p◖𝗱k).
 // qed.
 
 lemma lift_path_m_dx (f) (p):
-      (↑[f]p)◖𝗺 = ↑[f](p◖𝗺).
+      (🠡[f]p)◖𝗺 = 🠡[f](p◖𝗺).
 // qed.
 
 lemma lift_path_L_dx (f) (p):
-      (↑[f]p)◖𝗟 = ↑[f](p◖𝗟).
+      (🠡[f]p)◖𝗟 = 🠡[f](p◖𝗟).
 // qed.
 
 lemma lift_path_A_dx (f) (p):
-      (↑[f]p)◖𝗔 = ↑[f](p◖𝗔).
+      (🠡[f]p)◖𝗔 = 🠡[f](p◖𝗔).
 // qed.
 
 lemma lift_path_S_dx (f) (p):
-      (↑[f]p)◖𝗦 = ↑[f](p◖𝗦).
+      (🠡[f]p)◖𝗦 = 🠡[f](p◖𝗦).
 // qed.
 
 (* Constructions with path_append *******************************************)
 
 lemma lift_path_append (f) (p) (q):
-      (↑[f]p)●(↑[↑[p]f]q) = ↑[f](p●q).
+      (🠡[f]p)●(🠡[🠢[f]p]q) = 🠡[f](p●q).
 #f #p #q elim q -q //
 #l #q #IH
 <lift_path_rcons <lift_path_rcons
@@ -70,42 +70,42 @@ qed.
 (* Constructions with path_lcons ********************************************)
 
 lemma lift_path_lcons (f) (p) (l):
-      (↑[f]l)◗↑[↑[l]f]p = ↑[f](l◗p).
+      (🠡[f]l)◗🠡[🠢[f]l]p = 🠡[f](l◗p).
 #f #p #l
 <lift_path_append //
 qed.
 
 lemma lift_path_d_sn (f) (p) (k:pnat):
-      (𝗱(f＠⧣❨k❩)◗↑[⇂*[k]f]p) = ↑[f](𝗱k◗p).
+      (𝗱(f＠⧣❨k❩)◗🠡[⇂*[k]f]p) = 🠡[f](𝗱k◗p).
 // qed.
 
 lemma lift_path_m_sn (f) (p):
-      (𝗺◗↑[f]p) = ↑[f](𝗺◗p).
+      (𝗺◗🠡[f]p) = 🠡[f](𝗺◗p).
 // qed.
 
 lemma lift_path_L_sn (f) (p):
-      (𝗟◗↑[⫯f]p) = ↑[f](𝗟◗p).
+      (𝗟◗🠡[⫯f]p) = 🠡[f](𝗟◗p).
 // qed.
 
 lemma lift_path_A_sn (f) (p):
-      (𝗔◗↑[f]p) = ↑[f](𝗔◗p).
+      (𝗔◗🠡[f]p) = 🠡[f](𝗔◗p).
 // qed.
 
 lemma lift_path_S_sn (f) (p):
-      (𝗦◗↑[f]p) = ↑[f](𝗦◗p).
+      (𝗦◗🠡[f]p) = 🠡[f](𝗦◗p).
 // qed.
 
 (* Basic inversions *********************************************************)
 
 lemma lift_path_inv_empty (f) (p):
-      (𝐞) = ↑[f]p → 𝐞 = p.
+      (𝐞) = 🠡[f]p → 𝐞 = p.
 #f * // #p #l
 <lift_path_rcons #H0 destruct
 qed-.
 
 lemma lift_path_inv_rcons (f) (p2) (q1) (l1):
-      q1◖l1 = ↑[f]p2 →
-      ∃∃q2,l2. q1 = ↑[f]q2 & l1 = ↑[↑[q2]f]l2 & q2◖l2 = p2.
+      q1◖l1 = 🠡[f]p2 →
+      ∃∃q2,l2. q1 = 🠡[f]q2 & l1 = 🠡[🠢[f]q2]l2 & q2◖l2 = p2.
 #f * [| #l2 #q2 ] #q1 #l1
 [ <lift_path_empty
 | <lift_path_rcons
@@ -117,8 +117,8 @@ qed-.
 (* Inversions with path_append **********************************************)
 
 lemma lift_path_inv_append_sn (f) (q1) (r1) (p2):
-      q1●r1 = ↑[f]p2 →
-      ∃∃q2,r2. q1 = ↑[f]q2 & r1 = ↑[↑[q2]f]r2 & q2●r2 = p2.
+      q1●r1 = 🠡[f]p2 →
+      ∃∃q2,r2. q1 = 🠡[f]q2 & r1 = 🠡[🠢[f]q2]r2 & q2●r2 = p2.
 #f #q1 #r1 elim r1 -r1 [| #l1 #r1 #IH ] #p2
 [ <list_append_empty_sn #H0 destruct
   /2 width=5 by ex3_2_intro/
@@ -132,7 +132,7 @@ qed-.
 (* Main inversions **********************************************************)
 
 theorem lift_path_inj (f) (p1) (p2):
-        ↑[f]p1 = ↑[f]p2 → p1 = p2.
+        🠡[f]p1 = 🠡[f]p2 → p1 = p2.
 #f #p1 elim p1 -p1 [| #l1 #q1 #IH ] #p2
 [ <lift_path_empty #H0
   <(lift_path_inv_empty … H0) -H0 //

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
index 38bded30e911fd4b95576fe8ce9fa00a308d3aff..ec54cdedf483d044d551f39e17010ff00007a0d7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
@@ -20,7 +20,7 @@ include "delayed_updating/substitution/prelift_label_after.ma".
 (* Constructions with tr_after **********************************************)
 
 lemma lift_path_after (g) (f) (p):
-      ↑[g]↑[f]p = ↑[g∘f]p.
+      🠡[g]🠡[f]p = 🠡[g∘f]p.
 #g #f #p elim p -p //
 #l #p #IH
 <lift_path_rcons <lift_path_rcons  <IH -IH //

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma
index 0c2aa6219efe4b7a219d20d9e363c920bc50d218..980185f936eb6ac175c71955d73a27de44e3e47d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_closed.ma
@@ -21,7 +21,7 @@ include "ground/relocation/xap.ma".
 (* Constructions with pcc ***************************************************)
 
 lemma lift_path_closed (o) (f) (q) (n):
-      q ϵ 𝐂❨o,n❩ → ↑[f]q ϵ 𝐂❨o,↑[q]f＠❨n❩❩.
+      q ϵ 𝐂❨o,n❩ → 🠡[f]q ϵ 𝐂❨o,🠢[f]q＠❨n❩❩.
 #o #f #q #n #H0 elim H0 -q -n //
 #q #n [ #k #Ho ] #_ #IH
 /2 width=1 by pcc_m_dx, pcc_L_dx, pcc_A_dx, pcc_S_dx/
@@ -29,14 +29,14 @@ lemma lift_path_closed (o) (f) (q) (n):
 qed.
 
 lemma lift_path_rmap_closed (o) (f) (p) (q) (n):
-      q ϵ 𝐂❨o,n❩ → ↑[↑[p]f]q ϵ 𝐂❨o,↑[p●q]f＠❨n❩❩.
+      q ϵ 𝐂❨o,n❩ → 🠡[🠢[f]p]q ϵ 𝐂❨o,🠢[f](p●q)＠❨n❩❩.
 /2 width=1 by lift_path_closed/
 qed.
 
 lemma lift_path_rmap_closed_L (o) (f) (p) (q) (n):
-      q ϵ 𝐂❨o,n❩ → ↑[↑[p◖𝗟]f]q ϵ 𝐂❨o,↑[p●𝗟◗q]f＠§❨n❩❩.
+      q ϵ 𝐂❨o,n❩ → 🠡[🠢[f](p◖𝗟)]q ϵ 𝐂❨o,🠢[f](p●𝗟◗q)＠§❨n❩❩.
 #o #f #p #q #n #Hq
-lapply (lift_path_closed … (↑[p◖𝗟]f) … Hq) #Hq0
+lapply (lift_path_closed … (🠢[f](p◖𝗟)) … Hq) #Hq0
 lapply (pcc_L_sn … Hq) -Hq #Hq1
 lapply (lift_path_rmap_closed … f p … Hq1) -Hq1
 <lift_path_L_sn >lift_rmap_L_dx #Hq1

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_eq.ma
index b9574e479e2a1115f0846aa5b09cad2d387b148e..9de1d40d77a5ebca0f5daf105aae5c657ee22236 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_eq.ma
@@ -21,7 +21,7 @@ include "delayed_updating/substitution/prelift_label_eq.ma".
 (* Constructions with path_eq ***********************************************)
 
 lemma lift_path_eq_repl (p):
-      stream_eq_repl … (λf1,f2. ↑[f1]p = ↑[f2]p).
+      stream_eq_repl … (λf1,f2. 🠡[f1]p = 🠡[f2]p).
 #p elim p -p //
 #l #p #IH #f1 #f2 #Hf
 <lift_path_rcons <lift_path_rcons

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma
index 665b5f9a64cf206d725988fce66515b991fe1d4d..20408487bf7564bfcda64795e41acab257c723a2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma
@@ -21,7 +21,7 @@ include "delayed_updating/substitution/prelift_label_id.ma".
 (* Constructions with tr_id *************************************************)
 
 lemma lift_path_id (p):
-      p = ↑[𝐢]p.
+      p = 🠡[𝐢]p.
 #p elim p -p //
 #l #p #IH
 <lift_path_rcons //

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma
index 635a13e1db8174be04c1a63d7aa780d50d8c546e..cd68cacb8342883151b8ebd5bb72c9b5717a6166 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma
@@ -20,7 +20,7 @@ include "ground/lib/list_length.ma".
 (* Constructions with list_length *******************************************)
 
 lemma lift_path_length (f) (p):
-      ❘p❘ = ❘↑[f]p❘.
+      ❘p❘ = ❘🠡[f]p❘.
 #f #p elim p -p // * [ #k ] #p #IH
 [ <lift_path_d_dx
 | <lift_path_m_dx

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma
index c87020d2fc9a1683408587718b8b9d918692c2c0..69ea8796df54729eb3c1542667dc0577be017fd5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma
@@ -20,7 +20,7 @@ include "delayed_updating/syntax/path_proper.ma".
 (* Constructions with proper condition for path *****************************)
 
 lemma lift_path_proper (f) (p):
-      p ϵ 𝐏 → ↑[f]p ϵ 𝐏.
+      p ϵ 𝐏 → 🠡[f]p ϵ 𝐏.
 #f *
 [ #H0 elim (ppc_inv_empty … H0)
 | * [ #k ] #p #_
@@ -37,7 +37,7 @@ qed.
 (* Inversions with proper condition for path ********************************)
 
 lemma lift_path_inv_proper (f) (p):
-      ↑[f]p ϵ 𝐏 → p ϵ 𝐏.
+      🠡[f]p ϵ 𝐏 → p ϵ 𝐏.
 #f * //
 #H0 elim (ppc_inv_empty … H0)
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma
index f4b7bdd0ec79f99e1a2cffda4ff0c0cedfa0bc95..08b014bee74572e1dc37caff1de840729d0ca0c7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma
@@ -20,7 +20,7 @@ include "delayed_updating/syntax/path_structure.ma".
 (* Constructions with structure *********************************************)
 
 lemma structure_lift_path (f) (p):
-      ⊗p = ⊗↑[f]p.
+      ⊗p = ⊗🠡[f]p.
 #f #p elim p -p //
 * [ #k ] #p #IH //
 [ <lift_path_d_dx <structure_d_dx <structure_d_dx //
@@ -29,7 +29,7 @@ lemma structure_lift_path (f) (p):
 qed.
 
 lemma lift_path_structure (f) (p):
-      ⊗p = ↑[f]⊗p.
+      ⊗p = 🠡[f]⊗p.
 #f #p elim p -p //
 * [ #k ] #p #IH //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
index 0943306582c4203738402c9e571cd6215620026a..841e706d63c0cad6570cb89f0a96abd69c1f69e5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
@@ -22,7 +22,7 @@ include "ground/arith/nat_pred_succ.ma".
 (* Constructions with tr_uni ************************************************)
 
 lemma lift_path_d_sn_uni (p) (n) (k):
-      (𝗱(k+n)◗p) = ↑[𝐮❨n❩](𝗱k◗p).
+      (𝗱(k+n)◗p) = 🠡[𝐮❨n❩](𝗱k◗p).
 #p #n #k
 <lift_path_d_sn <tr_uni_pap >nsucc_pnpred
 <tr_tls_succ_uni //

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
index 094cf676f32399a935d4d6e15cdd9d31f0aa4e1e..b8127eaaeac92c2cf5599756db47a4b439ec4335 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
@@ -20,11 +20,11 @@ include "ground/lib/subset_ext.ma".
 
 interpretation
   "lift (prototerm)"
-  'UpArrow f t = (subset_ext_f1 ? ? (lift_path f) t).
+  'UpTriangleArrow f t = (subset_ext_f1 ? ? (lift_path f) t).
 
 (* Basic constructions ******************************************************)
 
 lemma in_comp_lift_path_term (f) (t) (p):
-      p ϵ t → ↑[f]p ϵ ↑[f]t.
+      p ϵ t → 🠡[f]p ϵ 🠡[f]t.
 /2 width=1 by subset_in_ext_f1_dx/
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_after.ma
index 862e2d4cb8580109087238b9360963167b843427..95784343110555dd5f0fb5d41cbb6c0b8cec8f66 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_after.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_after.ma
@@ -20,7 +20,7 @@ include "delayed_updating/substitution/lift_path_after.ma".
 (* Constructions with tr_after **********************************************)
 
 lemma lift_term_after (f) (g) (t):
-      ↑[g]↑[f]t ⇔ ↑[g∘f]t.
+      🠡[g]🠡[f]t ⇔ 🠡[g∘f]t.
 #f #g #t @subset_eq_trans
 [
 | @subset_inclusion_ext_f1_compose

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
index d23c7f058de4ebdcb26b6b2b3d3cb030485e586c..70d41140bd2d28c7c71b5cd993b5a8c4ea2e42b0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
@@ -22,23 +22,23 @@ include "delayed_updating/substitution/lift_prototerm.ma".
 (* Constructions with subset_equivalence ************************************)
 
 lemma lift_term_eq_repl_sn (f1) (f2) (t):
-      f1 ≗ f2 → ↑[f1]t ⇔ ↑[f2]t.
+      f1 ≗ f2 → 🠡[f1]t ⇔ 🠡[f2]t.
 /3 width=1 by subset_equivalence_ext_f1_exteq, lift_path_eq_repl/
 qed.
 
 lemma lift_term_eq_repl_dx (f) (t1) (t2):
-      t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
+      t1 ⇔ t2 → 🠡[f]t1 ⇔ 🠡[f]t2.
 /2 width=1 by subset_equivalence_ext_f1_bi/
 qed.
 
 lemma lift_term_grafted_sn (f) (t) (p):
-      ↑[↑[p]f](t⋔p) ⊆ (↑[f]t)⋔(↑[f]p).
+      🠡[🠢[f]p](t⋔p) ⊆ (🠡[f]t)⋔(🠡[f]p).
 #f #t #p #q * #r #Hr #H0 destruct
 /2 width=3 by ex2_intro/
 qed-.
 
 lemma lift_term_grafted_dx (f) (t) (p):
-      (↑[f]t)⋔(↑[f]p) ⊆ ↑[↑[p]f](t⋔p).
+      (🠡[f]t)⋔(🠡[f]p) ⊆ 🠡[🠢[f]p](t⋔p).
 #f #t #p #q * #r #Hr #H0
 elim (lift_path_inv_append_sn … (sym_eq … H0)) -H0
 #p0 #q0 #Hp0 #Hq0 #H0 destruct
@@ -47,9 +47,9 @@ lapply (lift_path_inj … Hp0) -Hp0 #Hp0 destruct
 qed-.
 
 lemma lift_term_grafted (f) (t) (p):
-      ↑[↑[p]f](t⋔p) ⇔ (↑[f]t)⋔(↑[f]p).
+      🠡[🠢[f]p](t⋔p) ⇔ (🠡[f]t)⋔(🠡[f]p).
 /3 width=1 by lift_term_grafted_sn, lift_term_grafted_dx, conj/ qed.
 
 lemma lift_term_grafted_S (f) (t) (p):
-      ↑[↑[p]f](t⋔(p◖𝗦)) ⇔ (↑[f]t)⋔((↑[f]p)◖𝗦).
+      🠡[🠢[f]p](t⋔(p◖𝗦)) ⇔ (🠡[f]t)⋔((🠡[f]p)◖𝗦).
 // qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
index 95aecceb75421f2428db4d35f48c2fa77e85cc96..401e2f2ce33425280df558fd061c15e2c6a40cb0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
@@ -20,18 +20,18 @@ include "delayed_updating/substitution/lift_path_id.ma".
 (* Constructions with tr_id *************************************************)
 
 lemma lift_term_id_sn (t):
-      t ⊆ ↑[𝐢]t.
+      t ⊆ 🠡[𝐢]t.
 #t #p #Hp
 >(lift_path_id p)
 /2 width=1 by in_comp_lift_path_term/
 qed-.
 
 lemma lift_term_id_dx (t):
-      ↑[𝐢]t ⊆ t.
+      🠡[𝐢]t ⊆ t.
 #t #p * #q #Hq #H destruct //
 qed-.
 
 lemma lift_term_id (t):
-      t ⇔ ↑[𝐢]t.
+      t ⇔ 🠡[𝐢]t.
 /3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_proper.ma
index 45d65b3ff9c76d975c552913417d9a2c15273518..7e7236dbd3b6131778a21a8faf6bbdec20a9b11a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_proper.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_proper.ma
@@ -21,7 +21,7 @@ include "delayed_updating/syntax/prototerm_proper.ma".
 (* Constructions with proper condition for path *****************************)
 
 lemma lift_term_proper (f) (t):
-      t ϵ 𝐏 → ↑[f]t ϵ 𝐏.
+      t ϵ 𝐏 → 🠡[f]t ϵ 𝐏.
 #f #t #Ht #p * #q #Hq #H0 destruct
 @lift_path_proper @Ht -Ht // (**) (* auto fails *)
 qed.
@@ -29,7 +29,7 @@ qed.
 (* Inversions with proper condition for path ********************************)
 
 lemma lift_term_inv_proper (f) (t):
-      ↑[f]t ϵ 𝐏 → t ϵ 𝐏.
+      🠡[f]t ϵ 𝐏 → t ϵ 𝐏.
 #f #t #Ht #p #Hp
 @(lift_path_inv_proper f)
 @Ht -Ht @in_comp_lift_path_term // (**) (* auto fails *)

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap.ma
index 85f41d4891fefa06276ffc1c93b3e2692652b7d1..0e0bbb70210e5ce8e7effd59f5920a7f4cff31e0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap.ma
@@ -20,72 +20,72 @@ include "delayed_updating/syntax/path.ma".
 rec definition lift_rmap (f) (p) on p: tr_map ≝
 match p with
 [ list_empty     ⇒ f
-| list_lcons l q ⇒ ↑[l](lift_rmap f q)
+| list_lcons l q ⇒ 🠢[lift_rmap f q]l
 ].
 
 interpretation
   "lift (relocation map)"
-  'UpArrow p f = (lift_rmap f p).
+  'RightTriangleArrow f p = (lift_rmap f p).
 
 (* Basic constructions ******************************************************)
 
 lemma lift_rmap_empty (f):
-      f = ↑[𝐞]f.
+      f = 🠢[f]𝐞.
 // qed.
 
 lemma lift_rmap_rcons (f) (p) (l):
-      ↑[l]↑[p]f = ↑[p◖l]f.
+      🠢[🠢[f]p]l = 🠢[f](p◖l).
 // qed.
 
 lemma lift_rmap_d_dx (f) (p) (k:pnat):
-      ⇂*[k](↑[p]f) = ↑[p◖𝗱k]f.
+      ⇂*[k](🠢[f]p) = 🠢[f](p◖𝗱k).
 // qed.
 
 lemma lift_rmap_m_dx (f) (p):
-      ↑[p]f = ↑[p◖𝗺]f.
+      🠢[f]p = 🠢[f](p◖𝗺).
 // qed.
 
 lemma lift_rmap_L_dx (f) (p):
-      (⫯↑[p]f) = ↑[p◖𝗟]f.
+      (⫯🠢[f]p) = 🠢[f](p◖𝗟).
 // qed.
 
 lemma lift_rmap_A_dx (f) (p):
-      ↑[p]f = ↑[p◖𝗔]f.
+      🠢[f]p = 🠢[f](p◖𝗔).
 // qed.
 
 lemma lift_rmap_S_dx (f) (p):
-      ↑[p]f = ↑[p◖𝗦]f.
+      🠢[f]p = 🠢[f](p◖𝗦).
 // qed.
 
 (* Constructions with path_append *******************************************)
 
 lemma lift_rmap_append (p) (q) (f):
-      ↑[q]↑[p]f = ↑[p●q]f.
+      🠢[🠢[f]p]q = 🠢[f](p●q).
 #p #q elim q -q //
 qed.
 
 (* Constructions with path_lcons ********************************************)
 
 lemma lift_rmap_lcons (f) (p) (l):
-      ↑[p]↑[l]f = ↑[l◗p]f.
+      🠢[🠢[f]l]p = 🠢[f](l◗p).
 // qed.
 
 lemma lift_rmap_d_sn (f) (p) (k:pnat):
-      ↑[p](⇂*[k]f) = ↑[𝗱k◗p]f.
+      🠢[⇂*[k]f]p = 🠢[f](𝗱k◗p).
 // qed.
 
 lemma lift_rmap_m_sn (f) (p):
-      ↑[p]f = ↑[𝗺◗p]f.
+      🠢[f]p = 🠢[f](𝗺◗p).
 // qed.
 
 lemma lift_rmap_L_sn (f) (p):
-      ↑[p](⫯f) = ↑[𝗟◗p]f.
+      🠢[⫯f]p = 🠢[f](𝗟◗p).
 // qed.
 
 lemma lift_rmap_A_sn (f) (p):
-      ↑[p]f = ↑[𝗔◗p]f.
+      🠢[f]p = 🠢[f](𝗔◗p).
 // qed.
 
 lemma lift_rmap_S_sn (f) (p):
-      ↑[p]f = ↑[𝗦◗p]f.
+      🠢[f]p = 🠢[f](𝗦◗p).
 // qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_after.ma
index e209f97a70e39bdc926135c13fb78e5414e76a52..e3dd359b087a311bc2ebbe8684754bcd97e3b3e6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_after.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_after.ma
@@ -20,7 +20,7 @@ include "delayed_updating/substitution/lift_path.ma".
 (* Constructions with tr_after **********************************************)
 
 lemma lift_rmap_after (g) (f) (p:path):
-      ↑[↑[f]p]g∘↑[p]f = ↑[p](g∘f).
+      🠢[g]🠡[f]p∘🠢[f]p = 🠢[g∘f]p.
 #g #f #p elim p -p //
 #l #p #IH
 <lift_rmap_rcons //

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
index 56abc470717544ad2e53d3aa681608f48a349dcf..1fd176270d332f83b81c716b3c99649e6d9d4c79 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_closed.ma
@@ -22,7 +22,7 @@ include "ground/lib/stream_eq_eq.ma".
 
 lemma tls_plus_lift_rmap_closed (o) (f) (q) (n):
       q ϵ 𝐂❨o,n❩ →
-      ∀m. ⇂*[m]f ≗ ⇂*[m+n]↑[q]f.
+      ∀m. ⇂*[m]f ≗ ⇂*[m+n]🠢[f]q.
 #o #f #q #n #Hq elim Hq -q -n //
 #q #n #_ #IH #m
 <nplus_succ_dx <stream_tls_swap //
@@ -30,14 +30,14 @@ qed-.
 
 lemma tls_lift_rmap_closed (o) (f) (q) (n):
       q ϵ 𝐂❨o,n❩ →
-      f ≗ ⇂*[n]↑[q]f.
+      f ≗ ⇂*[n]🠢[f]q.
 #o #f #q #n #H0
 /2 width=2 by tls_plus_lift_rmap_closed/
 qed-.
 
 lemma tls_succ_lift_rmap_append_L_closed_dx (o) (f) (p) (q) (n):
       q ϵ 𝐂❨o,n❩ →
-      ↑[p]f ≗ ⇂*[↑n]↑[p●𝗟◗q]f.
+      🠢[f]p ≗ ⇂*[↑n]🠢[f](p●𝗟◗q).
 #o #f #p #q #n #Hq
 /3 width=2 by tls_lift_rmap_closed, pcc_L_sn/
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_eq.ma
index bf5151f00a852df4b855705ad94817cea27b2e88..790b2e6054c0734ff88c98484494ce4301154b7a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_eq.ma
@@ -23,14 +23,14 @@ include "ground/arith/nat_rplus_pplus.ma".
 (* Constructions with lift_eq ***********************************************)
 
 lemma lift_rmap_eq_repl (p):
-      stream_eq_repl … (λf1,f2. ↑[p]f1 ≗ ↑[p]f2).
+      stream_eq_repl … (λf1,f2. 🠢[f1]p ≗ 🠢[f2]p).
 #p elim p -p //
 #l #p #IH #f1 #f2 #Hf
 /3 width=1 by prelift_rmap_eq_repl/
 qed.
 
 lemma tls_lift_rmap_d_dx (f) (p) (n) (k):
-      ⇂*[n+k]↑[p]f ≗ ⇂*[n]↑[p◖𝗱k]f.
+      ⇂*[n+k]🠢[f]p ≗ ⇂*[n]🠢[f](p◖𝗱k).
 #f #p #n #k
 <lift_rmap_d_dx >nrplus_inj_dx >nrplus_inj_sn //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
index 98d4ab3952e870c4f66f60dfa5f1e91a232fad8e..28eee66dc512a83cc3165c1e4ce84d72a9366086 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
@@ -20,6 +20,6 @@ include "delayed_updating/substitution/prelift_rmap_id.ma".
 (* Constructions with tr_id *************************************************)
 
 lemma lift_rmap_id (p):
-      (𝐢) = ↑[p]𝐢.
+      (𝐢) = 🠢[𝐢]p.
 #p elim p -p //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_pap.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_pap.ma
index 6e1b39255e0d6c9d4b66e9dc5deaa3af43977839..4239d0c446d4ea5c85c1c115247ece48489ab937 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_pap.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_pap.ma
@@ -20,5 +20,5 @@ include "ground/relocation/tr_pap_tls.ma".
 (* Constructions with tr_pap ************************************************)
 
 lemma lift_rmap_pap_d_dx (f) (p) (k) (h):
-      ↑[p]f＠⧣❨h+k❩ = ↑[p◖𝗱k]f＠⧣❨h❩+↑[p]f＠⧣❨k❩.
+      🠢[f]p＠⧣❨h+k❩ = 🠢[f](p◖𝗱k)＠⧣❨h❩+🠢[f]p＠⧣❨k❩.
 // qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma
index be57d860180a561ba424518e904d247acca207d1..8dc8af8f8448c1bd4ca693fc2ee4304eb34075fd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/notation/functions/uparrow_2.ma".
+include "delayed_updating/notation/functions/uptrianglearrow_2.ma".
 include "delayed_updating/syntax/label.ma".
 include "ground/relocation/tr_pap_pap.ma".
 
@@ -29,34 +29,34 @@ match l with
 
 interpretation
   "prelift (label)"
-  'UpArrow f l = (prelift_label f l).
+  'UpTriangleArrow f l = (prelift_label f l).
 
 (* Basic constructions ******************************************************)
 
 lemma prelift_label_d (f) (k):
-      (𝗱(f＠⧣❨k❩)) = ↑[f]𝗱k.
+      (𝗱(f＠⧣❨k❩)) = 🠡[f]𝗱k.
 // qed.
 
 lemma prelift_label_m (f):
-      (𝗺) = ↑[f]𝗺.
+      (𝗺) = 🠡[f]𝗺.
 // qed.
 
 lemma prelift_label_L (f):
-      (𝗟) = ↑[f]𝗟.
+      (𝗟) = 🠡[f]𝗟.
 // qed.
 
 lemma prelift_label_A (f):
-      (𝗔) = ↑[f]𝗔.
+      (𝗔) = 🠡[f]𝗔.
 // qed.
 
 lemma prelift_label_S (f):
-      (𝗦) = ↑[f]𝗦.
+      (𝗦) = 🠡[f]𝗦.
 // qed.
 
 (* Basic inversions *********************************************************)
 
 lemma prelift_label_inv_d_sn (f) (l) (k1):
-      (𝗱k1) = ↑[f]l →
+      (𝗱k1) = 🠡[f]l →
       ∃∃k2. k1 = f＠⧣❨k2❩ & 𝗱k2 = l.
 #f * [ #k ] #k1
 [ <prelift_label_d
@@ -69,7 +69,7 @@ lemma prelift_label_inv_d_sn (f) (l) (k1):
 qed-.
 
 lemma prelift_label_inv_m_sn (f) (l):
-      (𝗺) = ↑[f]l → 𝗺 = l.
+      (𝗺) = 🠡[f]l → 𝗺 = l.
 #f * [ #k ]
 [ <prelift_label_d
 | <prelift_label_m
@@ -80,7 +80,7 @@ lemma prelift_label_inv_m_sn (f) (l):
 qed-.
 
 lemma prelift_label_inv_L_sn (f) (l):
-      (𝗟) = ↑[f]l → 𝗟 = l.
+      (𝗟) = 🠡[f]l → 𝗟 = l.
 #f * [ #k ]
 [ <prelift_label_d
 | <prelift_label_m
@@ -91,7 +91,7 @@ lemma prelift_label_inv_L_sn (f) (l):
 qed-.
 
 lemma prelift_label_inv_A_sn (f) (l):
-      (𝗔) = ↑[f]l → 𝗔 = l.
+      (𝗔) = 🠡[f]l → 𝗔 = l.
 #f * [ #k ]
 [ <prelift_label_d
 | <prelift_label_m
@@ -102,7 +102,7 @@ lemma prelift_label_inv_A_sn (f) (l):
 qed-.
 
 lemma prelift_label_inv_S_sn (f) (l):
-      (𝗦) = ↑[f]l → 𝗦 = l.
+      (𝗦) = 🠡[f]l → 𝗦 = l.
 #f * [ #k ]
 [ <prelift_label_d
 | <prelift_label_m
@@ -115,7 +115,7 @@ qed-.
 (* Main inversions **********************************************************)
 
 theorem prelift_label_inj (f) (l1) (l2):
-        ↑[f]l1 = ↑[f]l2 → l1 = l2.
+        🠡[f]l1 = 🠡[f]l2 → l1 = l2.
 #f * [ #k1 ] #l2 #Hl
 [ elim (prelift_label_inv_d_sn … Hl) -Hl #k2 #Hk #H0 destruct
   >(tr_pap_inj ???? Hk) -Hk //

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_after.ma
index 24720288b107923ac973a635d187dc51ec468e87..f43f1b647dcae9e90c756514e330ea5374c1df0a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_after.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_after.ma
@@ -20,6 +20,6 @@ include "ground/relocation/tr_compose_pap.ma".
 (* Constructions with tr_after **********************************************)
 
 lemma prelift_label_after (g) (f) (l):
-      ↑[g]↑[f]l = ↑[g∘f]l.
+      🠡[g]🠡[f]l = 🠡[g∘f]l.
 #g #f * [ #k ] //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_eq.ma
index bccba6675b606bb2954ce900538fecbe62649ad7..be012d6e0f33d585175a37426fe0d2f435601922 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_eq.ma
@@ -20,7 +20,7 @@ include "ground/relocation/tr_pap_eq.ma".
 (* constructions with tr_map_eq *********************************************)
 
 lemma prelift_label_eq_repl (l):
-      stream_eq_repl … (λf1,f2. ↑[f1]l = ↑[f2]l).
+      stream_eq_repl … (λf1,f2. 🠡[f1]l = 🠡[f2]l).
 * //
 #k #f1 #f2 #Hf
 <prelift_label_d <prelift_label_d

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_id.ma
index 8378a0f39877d3cc417fea1dae50dfbe547de6d7..17bff1bf6a38f8ba662fb26ac5ef7831d62ec47c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_id.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label_id.ma
@@ -20,6 +20,6 @@ include "ground/relocation/tr_id_pap.ma".
 (* Constructions with tr_id *************************************************)
 
 lemma prelift_label_id (l):
-      l = ↑[𝐢]l.
+      l = 🠡[𝐢]l.
 * [ #k ] //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap.ma
index dcec9b57a18a5080a9e3542faf88c5630537d762..94c358d1ba248d7bf1a2ed739f770495db79d3d7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/notation/functions/uparrow_2.ma".
+include "delayed_updating/notation/functions/righttrianglearrow_2.ma".
 include "delayed_updating/syntax/label.ma".
 include "ground/relocation/tr_pn.ma".
 include "ground/lib/stream_tls.ma".
@@ -30,26 +30,26 @@ match l with
 
 interpretation
   "prelift (relocation map)"
-  'UpArrow l f = (prelift_rmap f l).
+  'RightTriangleArrow f l = (prelift_rmap f l).
 
 (* Basic constructions ******************************************************)
 
 lemma prelift_rmap_d (f) (k:pnat):
-      ⇂*[k]f = ↑[𝗱k]f.
+      ⇂*[k]f = 🠢[f]𝗱k.
 // qed.
 
 lemma prelift_rmap_m (f):
-      f = ↑[𝗺]f.
+      f = 🠢[f]𝗺.
 // qed.
 
 lemma prelift_rmap_L (f):
-      (⫯f) = ↑[𝗟]f.
+      (⫯f) = 🠢[f]𝗟.
 // qed.
 
 lemma prelift_rmap_A (f):
-      f = ↑[𝗔]f.
+      f = 🠢[f]𝗔.
 // qed.
 
 lemma prelift_rmap_S (f):
-      f = ↑[𝗦]f.
+      f = 🠢[f]𝗦.
 // qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_after.ma
index 3e83fbbf8de3eeddf3a4cb0905c10df806679307..edb2ae01d3fa0ccd7b59e14c036f33aa68971f12 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_after.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_after.ma
@@ -22,7 +22,7 @@ include "ground/relocation/tr_compose_tls.ma".
 (* Constructions with tr_after **********************************************)
 
 lemma prelift_rmap_after (g) (f) (l):
-      ↑[↑[f]l]g∘↑[l]f = ↑[l](g∘f).
+      🠢[g]🠡[f]l∘🠢[f]l = 🠢[g∘f]l.
 #g #f * [ #k ] //
 <prelift_rmap_d //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_eq.ma
index c23c1a0a6f32d6b41b51b7eb411e29a0de406fe9..5089e60ea04b53a7af7eebb982b7363c0441ccc5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_eq.ma
@@ -21,6 +21,6 @@ include "ground/lib/stream_tls_eq.ma".
 (* constructions with tr_map_eq *********************************************)
 
 lemma prelift_rmap_eq_repl (l):
-      stream_eq_repl … (λf1,f2. ↑[l]f1 ≗ ↑[l]f2).
+      stream_eq_repl … (λf1,f2. 🠢[f1]l ≗ 🠢[f2]l).
 * //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_id.ma
index 0842044d34ad36afdcbacbe70b15978911c3da4e..2f3c4ad8025b287e04ebb0d51535be453bdc9dbe 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_id.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap_id.ma
@@ -20,6 +20,6 @@ include "ground/relocation/tr_id_tls.ma".
 (* Constructions with tr_id *************************************************)
 
 lemma prelift_rmap_id (l):
-      (𝐢) = ↑[l]𝐢.
+      (𝐢) = 🠢[𝐢]l.
 * [ #k ] //
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/preunwind2_rmap_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/preunwind2_rmap_lift.ma
index f5317dbf3964da57936f6474534b3d6db7340512..cc5b351ad71faca3183f97a272d5397c796aef3d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/preunwind2_rmap_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/preunwind2_rmap_lift.ma
@@ -25,7 +25,7 @@ include "ground/lib/stream_eq_eq.ma".
 (* Constructions with lift_path *********************************************)
 
 lemma preunwind2_lift_rmap_after (g) (f) (l):
-      ▶[g]↑[f]l∘↑[l]f ≗ ▶[g∘f]l.
+      ▶[g]🠡[f]l∘🠢[f]l ≗ ▶[g∘f]l.
 #g #f * // #k
 <prelift_label_d <prelift_rmap_d <preunwind2_rmap_d <preunwind2_rmap_d
 @(stream_eq_trans … (tr_compose_assoc …))

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
index 5af9e1664a4cd60d7b6b24b6ea475a2d10ac0d3b..140dd6f8ac6ec113df5c51562b258fc38f434292 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
@@ -21,7 +21,7 @@ include "delayed_updating/substitution/lift_path_structure.ma".
 (* Constructions with lift_path *********************************************)
 
 lemma lift_unwind2_path_after (g) (f) (p):
-      ↑[g]▼[f]p = ▼[g∘f]p.
+      🠡[g]▼[f]p = ▼[g∘f]p.
 #g #f * // * [ #k ] #p //
 <unwind2_path_d_dx <unwind2_path_d_dx <lift_path_d_dx
 <lift_path_structure >tr_compose_pap
@@ -29,7 +29,7 @@ lemma lift_unwind2_path_after (g) (f) (p):
 qed.
 
 lemma unwind2_lift_path_after (g) (f) (p):
-      ▼[g]↑[f]p = ▼[g∘f]p.
+      ▼[g]🠡[f]p = ▼[g∘f]p.
 #g #f * // * [ #k ] #p
 [ <unwind2_path_d_dx <unwind2_path_d_dx
   <structure_lift_path >tr_compose_pap

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma
index 5b18cfb17b9c18f8d66d695b7443c39dcaee62e9..251d7ba72199c9bfcd93615c9edd395a6da63572 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma
@@ -23,7 +23,7 @@ include "delayed_updating/unwind/unwind2_prototerm.ma".
 (* Constructions with lift_prototerm ****************************************)
 
 lemma lift_unwind2_term_after (f1) (f2) (t):
-      ↑[f2]▼[f1]t ⇔ ▼[f2∘f1]t.
+      🠡[f2]▼[f1]t ⇔ ▼[f2∘f1]t.
 #f1 #f2 #t @subset_eq_trans
 [| @subset_inclusion_ext_f1_compose ]
 @subset_equivalence_ext_f1_exteq #p
@@ -31,7 +31,7 @@ lemma lift_unwind2_term_after (f1) (f2) (t):
 qed.
 
 lemma unwind2_lift_term_after (f1) (f2) (t):
-      ▼[f2]↑[f1]t ⇔ ▼[f2∘f1]t.
+      ▼[f2]🠡[f1]t ⇔ ▼[f2∘f1]t.
 #f1 #f2 #t @subset_eq_trans
 [| @subset_inclusion_ext_f1_compose ]
 @subset_equivalence_ext_f1_exteq #p

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma
index 9dbc9ec5063b87fb05427fcc7d87d1b238429b21..0afdb349d8d324d103ebc3d0ff61d91f099c239d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_closed.ma
@@ -16,6 +16,7 @@ include "delayed_updating/unwind/unwind2_rmap_eq.ma".
 include "delayed_updating/syntax/path_closed.ma".
 include "delayed_updating/syntax/path_depth.ma".
 include "ground/relocation/xap.ma".
+include "ground/lib/stream_tls_plus.ma".
 include "ground/lib/stream_eq_eq.ma".
 include "ground/arith/nat_le_plus.ma".
 include "ground/arith/nat_le_pred.ma".
@@ -74,15 +75,32 @@ lemma unwind2_rmap_append_closed_Lq_dx_nap_depth (o) (f) (p) (q) (n):
 /2 width=2 by unwind2_rmap_push_closed_nap/
 qed-.
 
+lemma unwind2_rmap_append_closed_true_dx_xap_depth (f) (p) (q) (n):
+      q ϵ 𝐂❨Ⓣ,n❩ → ♭q = ▶[f](p●q)＠❨n❩.
+#f #p #q #n #Hq elim Hq -q -n //
+#q #n #k #Ho #_ #IH
+<unwind2_rmap_d_dx <tr_compose_xap
+>Ho // <tr_uni_xap_succ <Ho //
+qed-.
+
 lemma tls_succ_plus_unwind2_rmap_push_closed (o) (f) (q) (n):
       q ϵ 𝐂❨o,n❩ →
       ∀m. ⇂*[m]f ≗ ⇂*[↑(m+n)]▶[⫯f]q.
 #o #f #q #n #Hq elim Hq -q -n //
-#q #n [ #k #_ ] #_ #IH #m
-[ @(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
-  >nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold //
-| <unwind2_rmap_L_dx <nplus_succ_dx //
-]
+#q #n #k #_ #_ #IH #m
+@(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
+>nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold //
+qed-.
+
+lemma tls_plus_unwind2_rmap_closed_true (f) (q) (n):
+      q ϵ 𝐂❨Ⓣ,n❩ →
+      ∀m. ⇂*[m]f ≗ ⇂*[m+n]▶[f]q.
+#f #q #n #Hq elim Hq -q -n //
+#q #n #k #Ho #_ #IH #m
+>Ho // <nplus_succ_dx
+@(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
+>nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold
+>nplus_succ_dx <Ho //
 qed-.
 
 lemma tls_succ_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
@@ -91,6 +109,12 @@ lemma tls_succ_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
 /2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
 qed-.
 
+lemma tls_unwind2_rmap_append_closed_true_dx (f) (p) (q) (n):
+      q ϵ 𝐂❨Ⓣ,n❩ →
+      ▶[f]p ≗ ⇂*[n]▶[f](p●q).
+/2 width=1 by tls_plus_unwind2_rmap_closed_true/
+qed-.
+
 lemma unwind2_rmap_append_closed_Lq_dx_nap_plus (o) (f) (p) (q) (m) (n):
       q ϵ 𝐂❨o,n❩ →
       ▶[f]p＠❨m❩+♭q = ▶[f](p●𝗟◗q)＠§❨m+n❩.
@@ -100,3 +124,21 @@ lemma unwind2_rmap_append_closed_Lq_dx_nap_plus (o) (f) (p) (q) (m) (n):
 | /2 width=2 by unwind2_rmap_append_closed_Lq_dx_nap_depth/
 ]
 qed-.
+
+lemma unwind2_rmap_append_closed_bLq_dx_nap_plus (o) (f) (p) (b) (q) (m) (n):
+      b ϵ 𝐂❨Ⓣ,m❩ → q ϵ 𝐂❨o,n❩ →
+      ♭b+♭q = ▶[f](p●b●𝗟◗q)＠§❨m+n❩.
+#o #f #p #b #q #m #n #Hb #Hq
+>(unwind2_rmap_append_closed_true_dx_xap_depth f p … Hb) -Hb
+>(unwind2_rmap_append_closed_Lq_dx_nap_plus … Hq) -Hq //
+qed-.
+
+lemma tls_succ_plus_unwind2_rmap_append_closed_bLq_dx (o) (f) (p) (b) (q) (m) (n):
+      b ϵ 𝐂❨Ⓣ,m❩ → q ϵ 𝐂❨o,n❩ →
+      ▶[f]p ≗ ⇂*[↑(m+n)]▶[f](p●b●𝗟◗q).
+#o #f #p #b #q #m #n #Hb #Hq
+>nplus_succ_dx <stream_tls_plus
+@(stream_eq_trans … (tls_unwind2_rmap_append_closed_true_dx … Hb)) -Hb
+@stream_tls_eq_repl
+@(stream_eq_trans … (tls_succ_unwind2_rmap_append_closed_Lq_dx … Hq)) -Hq //
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_lift.ma
index 02c51eca2b0d2db805f05f77b76506c0ca75ee8d..b42274ef822c82248534dbcd6e3c7546d323b6e2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_lift.ma
@@ -23,7 +23,7 @@ include "delayed_updating/syntax/path_structure.ma".
 (* Constructions with lift_path *********************************************)
 
 lemma lift_unwind2_rmap_after (g) (f) (p):
-      ↑[⊗p]g∘▶[f]p ≗ ▶[g∘f]p.
+      🠢[g]⊗p∘▶[f]p ≗ ▶[g∘f]p.
 #g #f #p elim p -p //
 * [ #k ] #p #IH //
 [ <unwind2_rmap_d_dx <unwind2_rmap_d_dx
@@ -35,7 +35,7 @@ lemma lift_unwind2_rmap_after (g) (f) (p):
 qed.
 
 lemma unwind2_lift_rmap_after (g) (f) (p:path):
-      ▶[g]↑[f]p∘↑[p]f ≗ ▶[g∘f]p.
+      ▶[g]🠡[f]p∘🠢[f]p ≗ ▶[g∘f]p.
 #g #f #p elim p -p // #l #p #IH
 <lift_path_rcons <lift_rmap_rcons <unwind2_rmap_rcons <unwind2_rmap_rcons
 @(stream_eq_trans … (preunwind2_lift_rmap_after …))