From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Mon, 28 Mar 2022 23:11:32 +0000 (+0200)
Subject: WIP in delayed_updating
X-Git-Tag: make_still_working~78
X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=commitdiff_plain;h=aeec9312d6f72526a460518a1e889eac71657cdd

WIP in delayed_updating

+ we re focusing on a special case of the main theorem
---

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
index 3c328fcb2..576df6ec6 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❘ = (▼[r]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
+           ∧∧ (⊗b ϵ 𝐁 ∧ 𝟎 = ❘b❘) & ↑❘q❘ = (▼[r]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
               t1[⋔r←𝛗(n+❘b❘).(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 77e303f05..dd24f8568 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -20,6 +20,7 @@ include "delayed_updating/unwind1/unwind_preterm_eq.ma".
 include "delayed_updating/unwind1/unwind_structure_depth.ma".
 include "delayed_updating/unwind1/unwind_depth.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_structure_depth.ma".
 include "ground/relocation/tr_uni_compose.ma".
@@ -83,6 +84,11 @@ lemma dfr_unwind_id_bi (p) (q) (t1) (t2): t1 ϵ 𝐓 →
     <depth_append <depth_L_sn <depth_structure <depth_structure
     @fsubst_eq_repl [ // ]
     @(subset_eq_trans … (unwind_iref …))
+
+    elim Hb -Hb #Hb #H0 <H0 -H0 <nrplus_zero_dx <nplus_zero_dx <Hn
+    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+    [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
+
 (*
     @(subset_eq_canc_sn … (unwind_term_eq_repl_dx …))
     [ @unwind_grafted_S /2 width=2 by ex_intro/ | skip ]
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index 54ad4f2f6..8d0cfc52d 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -28,7 +28,7 @@ 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❘ = (▼[r]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
+           ∧∧ (⊗b ϵ 𝐁 ∧ 𝟎 = ❘b❘) & ↑❘q❘ = (▼[r]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
               t1[⋔r←↑[𝐮❨❘b●𝗟◗q❘❩](t1⋔(p◖𝗦))] ⇔ t2
 .