From ccbaf3fd118c7c6425b3572a057ccc2941b7762e Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sat, 25 Jun 2022 23:01:12 +0200
Subject: [PATCH] update in delayed_updating

+ some additions
+ minor improvements
---
 .../delayed_updating/reduction/dfr_ifr.ma     | 13 ++++----
 .../delayed_updating/reduction/ifr_unwind.ma  | 13 ++++----
 .../substitution/lift_rmap_id.ma              |  2 +-
 .../substitution/lift_rmap_prelift.ma         | 30 +++++++++++++++++++
 4 files changed, 43 insertions(+), 15 deletions(-)
 create mode 100644 matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_prelift.ma

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 92bd90699..e54dd2678 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -58,14 +58,13 @@ 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 *)
-    @nstream_eq_inv_ext #m
-    <tr_compose_pap <tr_compose_pap
-    <tr_uni_pap <tr_uni_pap <tr_pap_plus
     >list_append_rcons_sn in H1n; <reverse_append #H1n
-    lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
-    >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
-    lapply (tls_unwind2_rmap_append_closed f … H1n) -H1n #H2n
-    <(tr_pap_eq_repl … H2n) -H2n //
+    @(stream_eq_trans … (tr_compose_uni_dx …))
+    @tr_compose_eq_repl
+    [ <unwind2_rmap_append_pap_closed //
+    | >unwind2_rmap_A_sn <reverse_rcons
+      /2 width=1 by tls_unwind2_rmap_append_closed/
+    ]
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
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 13f6f3fa0..7d5769887 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
@@ -57,14 +57,13 @@ lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
     @(subset_eq_canc_dx … (unwind2_term_after_lift …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-    @nstream_eq_inv_ext #m
-    <tr_compose_pap <tr_compose_pap
-    <tr_uni_pap <tr_uni_pap <tr_pap_plus
     >list_append_rcons_sn in H1n; <reverse_append #H1n
-    lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
-    >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
-    lapply (tls_unwind2_rmap_append_closed f … H1n) -H1n #H2n
-    <(tr_pap_eq_repl … H2n) -H2n //
+    @(stream_eq_trans … (tr_compose_uni_dx …))
+    @tr_compose_eq_repl
+    [ <unwind2_rmap_append_pap_closed //
+    | >unwind2_rmap_A_sn <reverse_rcons
+      /2 width=1 by tls_unwind2_rmap_append_closed/
+    ]
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
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 077f90747..8787ecbb9 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
@@ -15,7 +15,7 @@
 include "delayed_updating/substitution/lift_gen.ma".
 include "ground/relocation/tr_id_tls.ma".
 
-(* LIFT FOR RELOCATION MAP  *************************************************)
+(* LIFT FOR RELOCATION MAP **************************************************)
 
 (* Constructions with proj_rmap and tr_id ***********************************)
 
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_prelift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_prelift.ma
new file mode 100644
index 000000000..ba6f96fcf
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_prelift.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/substitution/lift_gen.ma".
+include "delayed_updating/substitution/prelift_rmap.ma".
+
+(* LIFT FOR RELOCATION MAP **************************************************)
+
+(* Constructions with prelift_rmap ******************************************)
+
+lemma lift_rmap_lcons_prelift (f) (p) (l):
+      ↑[p]↑[l]f = ↑[l◗p]f.
+#f #p * [ #n ] //
+qed.
+
+lemma lift_rmap_rcons_prelift (f) (p) (l):
+      ↑[l]↑[p]f = ↑[p◖l]f.
+#f #p * [ #n ] //
+qed.
-- 
2.39.2