From 8d8863982ca95225551e9659ed431db046c34e81 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sun, 23 Jan 2022 23:01:15 +0100
Subject: [PATCH] update un delayed_updating

+ bugs fixed in dfr and ifr
---
 .../lambdadelta/delayed_updating/reduction/dfr.ma      |  2 +-
 .../lambdadelta/delayed_updating/reduction/dfr_ifr.ma  | 10 +++++-----
 .../lambdadelta/delayed_updating/reduction/ifr.ma      |  2 +-
 .../lambdadelta/delayed_updating/substitution/lift.ma  |  4 ++++
 4 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
index 67c22257b..3cdf0d47e 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
@@ -28,7 +28,7 @@ include "ground/xoa/and_4.ma".
 definition dfr (p) (q): relation2 prototerm prototerm ≝
            λt1,t2. ∃∃b,n.
            let r ≝ p●𝗔◗b●𝗟◗q in
-           ∧∧ ⊗b ϵ 𝐁 & ❘q❘ = (↑[q]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
+           ∧∧ ⊗b ϵ 𝐁 & ∀f. ❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
               t1[⋔r←𝛗n.(t1⋔(p◖𝗦))] ⇔ t2
 .
 
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 fb39e209a..a8d9469dd 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -18,8 +18,7 @@ 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".
+include "ground/relocation/tr_pap_pushs.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
@@ -29,9 +28,10 @@ lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
 * #b #n * #Hb #Hn  #Ht1 #Ht2
 @(ex1_2_intro … (⊗b) (❘⊗q❘)) @and4_intro
 [ //
-| //
-| lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2 #Ht1
-  <depth_structure
+| #g <lift_rmap_structure <depth_structure
+  >tr_pushs_swap <tr_pap_pushs_le //
+| lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
+  <lift_d_empty_dx //
 | lapply (eq_lift_bi f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (lift_fsubst …))
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index 2394523f5..ffa4f44bd 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -26,7 +26,7 @@ include "ground/xoa/and_4.ma".
 definition ifr (p) (q): relation2 prototerm prototerm ≝
            λt1,t2. ∃∃b,n.
            let r ≝ p●𝗔◗b●𝗟◗q in
-           ∧∧ ⊗b ϵ 𝐁 & ❘q❘ = (↑[q]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
+           ∧∧ ⊗b ϵ 𝐁 & ∀f. ❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
               t1[⋔r←↑[𝐮❨n❩](t1⋔(p◖𝗦))] ⇔ t2
 .
 
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
index fa6328684..3a6991a92 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -109,6 +109,10 @@ lemma lift_path_m_sn (f) (p):
 
 (* Basic constructions with proj_rmap ***************************************)
 
+lemma lift_rmap_empty (f):
+      f = ↑[𝐞]f.
+// qed.
+
 lemma lift_rmap_d_sn (f) (p) (n):
       ↑[p](f∘𝐮❨ninj n❩) = ↑[𝗱n◗p]f.
 #f * // qed.
-- 
2.39.2