update in delayed_updating

+ bugs fixed id dfr and ifr

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
index 2ff6159cf5603bcf4e3db95d43996ba4efad9713..67c22257b0ba0f92ed2c218fbaa2e7573b6dd939 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
@@ -12,21 +12,24 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/syntax/path_depth.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/syntax/path_balanced.ma".
 include "delayed_updating/syntax/prototerm_constructors.ma".
 include "delayed_updating/syntax/prototerm_equivalence.ma".
 include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/substitution/lift.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_depth.ma".
 include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
+include "ground/xoa/ex_1_2.ma".
+include "ground/xoa/and_4.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
 definition dfr (p) (q): relation2 prototerm prototerm ≝
-           λt1,t2. ∃b.
+           λt1,t2. ∃∃b,n.
            let r ≝ p●𝗔◗b●𝗟◗q in
-           ∧∧ ⊗b ϵ 𝐁 & r◖𝗱❘q❘ ϵ t1 &
-              t1[⋔r←𝛗❘q❘.(t1⋔(p◖𝗦))] ⇔ t2
+           ∧∧ ⊗b ϵ 𝐁 & ❘q❘ = (↑[q]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
+              t1[⋔r←𝛗n.(t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
index 73d4cbf46d3bab56b771232eda52d6864e9482c8..fb39e209a0191ad66309ebb3810b17fc07037cae 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -15,17 +15,23 @@
 include "delayed_updating/reduction/dfr.ma".
 include "delayed_updating/reduction/ifr.ma".
 include "delayed_updating/substitution/fsubst_lift.ma".
+include "delayed_updating/substitution/lift_structure_depth.ma".
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+include "delayed_updating/syntax/path_structure_depth.ma".
+include "ground/relocation/tr_id_pap.ma".
+include "ground/relocation/tr_id_pushs.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
 lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
       t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
 #f #p #q #t1 #t2 #H0t1
-* #b * #Hb #Ht1 #Ht2
-@(ex_intro … (⊗b)) @and3_intro
+* #b #n * #Hb #Hn  #Ht1 #Ht2
+@(ex1_2_intro … (⊗b) (❘⊗q❘)) @and4_intro
 [ //
-| lapply (in_comp_lift_bi f … Ht1) -Ht1 #Ht1
+| //
+| lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2 #Ht1
+  <depth_structure
 | lapply (eq_lift_bi f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (lift_fsubst …))
@@ -35,5 +41,3 @@ lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
   | //
   ]
 ]
-  
-

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index b58f9ee185d40458dac3ea3baf30906a03cb1825..2394523f5c26de3cd3af0685823e78f059fec30d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -12,20 +12,22 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/substitution/lift_prototerm.ma".
 include "delayed_updating/syntax/path_depth.ma".
 include "delayed_updating/syntax/path_structure.ma".
 include "delayed_updating/syntax/path_balanced.ma".
-include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/substitution/lift_prototerm.ma".
 include "delayed_updating/notation/relations/black_rightarrow_f_4.ma".
+include "ground/xoa/ex_1_2.ma".
+include "ground/xoa/and_4.ma".
 
 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
 
 definition ifr (p) (q): relation2 prototerm prototerm ≝
-           λt1,t2. ∃b.
+           λt1,t2. ∃∃b,n.
            let r ≝ p●𝗔◗b●𝗟◗q in
-           ∧∧ ⊗b ϵ 𝐁 & r◖𝗱❘q❘ ϵ t1 &
-              t1[⋔r←↑[𝐮❨❘q❘❩](t1⋔(p◖𝗦))] ⇔ t2
+           ∧∧ ⊗b ϵ 𝐁 & ❘q❘ = (↑[q]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
+              t1[⋔r←↑[𝐮❨n❩](t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure_depth.ma
new file mode 100644 (file)
index 0000000..ee42bfb
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure_depth.ma
@@ -0,0 +1,33 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/lift.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/relocation/tr_pushs.ma".
+include "ground/arith/nat_pred_succ.ma".
+
+(* LIFT FOR PATH ***********************************************************)
+
+(* Basic constructions with structure and depth ****************************)
+
+lemma lift_rmap_structure (p) (f):
+      (⫯*[↓❘p❘]f) = ↑[⊗p]f.
+#p elim p -p //
+* [ #n ] #p #IH #f //
+[ <lift_rmap_L_sn <IH -IH >tr_pushs_swap //
+| <lift_rmap_A_sn //
+| <lift_rmap_S_sn //
+]
+qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure_depth.ma
new file mode 100644 (file)
index 0000000..9858328
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure_depth.ma
@@ -0,0 +1,30 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
+
+(* STRUCTURE FOR PATH *******************************************************)
+
+(* Constructions with depth *************************************************)
+
+lemma depth_structure (p):
+      ❘p❘ = ❘⊗p❘.
+#p elim p -p //
+* [ #n ] #p #IH //
+[ <structure_L_sn <depth_L <depth_L //
+| <structure_A_sn <depth_A <depth_A //
+| <structure_S_sn <depth_S <depth_S //
+]
+qed.