From 74a8604e5d2d3ec2dc7e67b1e257812ce340da29 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Tue, 9 Aug 2022 23:02:25 +0200
Subject: [PATCH] commit in delayed_updating

+ reversing paths completed updating component "reduction"
---
 .../delayed_updating/reduction/dfr.ma         |  7 +++---
 .../delayed_updating/reduction/dfr_ifr.ma     | 20 +++++++---------
 .../delayed_updating/reduction/dfr_lift.ma    | 10 ++++----
 .../delayed_updating/reduction/ifr.ma         |  8 +++----
 .../delayed_updating/reduction/ifr_lift.ma    | 11 +++++----
 .../delayed_updating/reduction/ifr_unwind.ma  | 24 +++++++++----------
 6 files changed, 38 insertions(+), 42 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
index e0d17a691..135a48b1d 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
@@ -17,16 +17,15 @@ include "delayed_updating/syntax/prototerm_constructors.ma".
 include "delayed_updating/syntax/prototerm_eq.ma".
 include "delayed_updating/syntax/path_head.ma".
 include "delayed_updating/syntax/path_depth.ma".
-include "delayed_updating/syntax/path_reverse.ma".
 include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
 definition dfr (p) (q): relation2 prototerm prototerm ≝
-           λt1,t2. ∃n:pnat.
+           λt1,t2. ∃k:pnat.
            let r ≝ p●𝗔◗𝗟◗q in
-           ∧∧ (𝗟◗q)ᴿ = ↳[n](𝗟◗q)ᴿ & r◖𝗱n ϵ t1 &
-              t1[⋔r←𝛕n.(t1⋔(p◖𝗦))] ⇔ t2
+           ∧∧ 𝗟◗q = ↳[k](𝗟◗q) & r◖𝗱k ϵ t1 &
+              t1[⋔r←𝛕k.(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 2b15d3d52..638dad75b 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -27,8 +27,6 @@ include "delayed_updating/substitution/lift_prototerm_eq.ma".
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
 include "delayed_updating/syntax/path_head_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
-include "delayed_updating/syntax/path_structure_reverse.ma".
-include "delayed_updating/syntax/path_depth_reverse.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
@@ -37,16 +35,16 @@ include "delayed_updating/syntax/path_depth_reverse.ma".
 theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
         t1 ➡𝐝𝐟[p,q] t2 → ▼[f]t1 ➡𝐢𝐟[⊗p,⊗q] ▼[f]t2.
 #f #p #q #t1 #t2 #H0t1
-* #n * #H1n #Ht1 #Ht2
+* #k * #H1k #Ht1 #Ht2
 @(ex_intro … (↑♭q)) @and3_intro
 [ -H0t1 -Ht1 -Ht2
-  >structure_L_sn >structure_reverse
-  >H1n in ⊢ (??%?); >path_head_structure_depth <H1n -H1n //
+  >structure_L_sn
+  >H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
-  <unwind2_path_d_dx >(list_append_rcons_sn … p) <reverse_append
-  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔)ᴿ … H1n) -H1n
-  <reverse_lcons <depth_L_dx #H2n
-  lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n #Ht1 //
+  <unwind2_path_d_dx <list_append_rcons_sn
+  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔) … H1k) -H1k
+  <depth_L_sn #H2k
+  lapply (eq_inv_ninj_bi … H2k) -H2k #H2k <H2k -H2k #Ht1 //
 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (unwind2_term_fsubst …))
@@ -57,11 +55,11 @@ theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
     @(subset_eq_trans … (lift_unwind2_term_after …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-    >list_append_rcons_sn <reverse_append
+    <list_append_rcons_sn
     @(stream_eq_trans … (tr_compose_uni_dx …))
     @tr_compose_eq_repl
     [ <unwind2_rmap_append_pap_closed //
-    | >unwind2_rmap_A_sn <reverse_rcons
+    | >unwind2_rmap_A_dx
       /2 width=1 by tls_unwind2_rmap_closed/
     ]
 (* Note: crux of the proof ends *)
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 757497d4e..e8d26308e 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
@@ -27,12 +27,12 @@ include "delayed_updating/substitution/lift_rmap_head.ma".
 theorem dfr_lift_bi (f) (p) (q) (t1) (t2):
         t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐝𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
 #f #p #q #t1 #t2
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨n❩)) @and3_intro
+* #k * #H1k #Ht1 #Ht2
+@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨k❩)) @and3_intro
 [ -Ht1 -Ht2
   <lift_rmap_L_dx >lift_path_L_sn
-  <(lift_path_head … H1n) in ⊢ (??%?); -H1n //
-| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1n
+  <(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
@@ -43,7 +43,7 @@ theorem dfr_lift_bi (f) (p) (q) (t1) (t2):
   @(subset_eq_canc_sn … (lift_term_grafted_S …))
   @lift_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-  >list_append_rcons_sn in H1n; #H1n >lift_rmap_A_dx
+  >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 *)
 ]
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index 765387b1c..6ded5c377 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -16,16 +16,16 @@ 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_head.ma".
-include "delayed_updating/syntax/path_reverse.ma".
 include "delayed_updating/notation/relations/black_rightarrow_if_4.ma".
+include "ground/relocation/tr_uni.ma".
 
 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
 
 definition ifr (p) (q): relation2 prototerm prototerm ≝
-           λt1,t2. ∃n:pnat.
+           λt1,t2. ∃k:pnat.
            let r ≝ p●𝗔◗𝗟◗q in
-           ∧∧ (𝗟◗q)ᴿ = ↳[n](𝗟◗q)ᴿ & r◖𝗱n ϵ t1 &
-              t1[⋔r←↑[𝐮❨n❩](t1⋔(p◖𝗦))] ⇔ t2
+           ∧∧ 𝗟◗q = ↳[k](𝗟◗q) & r◖𝗱k ϵ t1 &
+              t1[⋔r←↑[𝐮❨k❩](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 0bf09b4aa..59c9dcc9e 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
@@ -16,6 +16,7 @@ include "delayed_updating/reduction/ifr.ma".
 
 include "delayed_updating/substitution/fsubst_lift.ma".
 include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_after.ma".
 include "delayed_updating/substitution/lift_path_head.ma".
 include "delayed_updating/substitution/lift_rmap_head.ma".
 
@@ -29,12 +30,12 @@ include "ground/relocation/tr_compose_eq.ma".
 theorem ifr_lift_bi (f) (p) (q) (t1) (t2):
         t1 ➡𝐢𝐟[p,q] t2 → ↑[f]t1 ➡𝐢𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
 #f #p #q #t1 #t2
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨n❩)) @and3_intro
+* #k * #H1k #Ht1 #Ht2
+@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨k❩)) @and3_intro
 [ -Ht1 -Ht2
   <lift_rmap_L_dx >lift_path_L_sn
-  <(lift_path_head … H1n) in ⊢ (??%?); -H1n //
-| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1n
+  <(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
@@ -48,7 +49,7 @@ theorem ifr_lift_bi (f) (p) (q) (t1) (t2):
 (* Note: crux of the proof begins *)
   @(stream_eq_trans … (tr_compose_uni_dx …))
   @tr_compose_eq_repl //
-  >list_append_rcons_sn in H1n; #H1n >lift_rmap_A_dx
+  >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 *)
 ]
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
index 6a135ea2e..a554bdbe2 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
@@ -25,27 +25,25 @@ include "delayed_updating/substitution/lift_prototerm_eq.ma".
 
 include "delayed_updating/syntax/path_head_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
-include "delayed_updating/syntax/path_structure_reverse.ma".
-include "delayed_updating/syntax/path_depth_reverse.ma".
 
 (* IMMEDIATE FOCUSED REDUCTION **********************************************)
 
-(* Constructions with unwind ************************************************)
+(* Constructions with unwind2 ***********************************************)
 
 lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
       t1 ϵ 𝐓 → t1⋔(p◖𝗦) ϵ 𝐏 →
       t1 ➡𝐢𝐟[p,q] t2 → ▼[f]t1 ➡𝐢𝐟[⊗p,⊗q] ▼[f]t2.
 #f #p #q #t1 #t2 #H1t1 #H2t1
-* #n * #H1n #Ht1 #Ht2
+* #k * #H1k #Ht1 #Ht2
 @(ex_intro … (↑♭q)) @and3_intro
 [ -H1t1 -H2t1 -Ht1 -Ht2
-  >structure_L_sn >structure_reverse
-  >H1n in ⊢ (??%?); >path_head_structure_depth <H1n -H1n //
+  >structure_L_sn
+  >H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2t1
-  <unwind2_path_d_dx >(list_append_rcons_sn … p) <reverse_append
-  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔)ᴿ … H1n) -H1n
-  <reverse_lcons <depth_L_dx #H2n
-  lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n #Ht1 //
+  <unwind2_path_d_dx <list_append_rcons_sn
+  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔) … H1k) -H1k
+  <depth_L_sn #H2k
+  lapply (eq_inv_ninj_bi … H2k) -H2k #H2k <H2k -H2k #Ht1 //
 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (unwind2_term_fsubst …))
@@ -53,14 +51,14 @@ lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
     @(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 …))
-    @(subset_eq_canc_dx … (unwind2_term_after_lift …))
+    @(subset_eq_canc_dx … (unwind2_lift_term_after …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-    >list_append_rcons_sn <reverse_append
+    <list_append_rcons_sn
     @(stream_eq_trans … (tr_compose_uni_dx …))
     @tr_compose_eq_repl
     [ <unwind2_rmap_append_pap_closed //
-    | >unwind2_rmap_A_sn <reverse_rcons
+    | >unwind2_rmap_A_dx
       /2 width=1 by tls_unwind2_rmap_closed/
     ]
 (* Note: crux of the proof ends *)
-- 
2.39.2