From d89ef541a62a996a7e7fa4d4a1cfc3b28d7862e5 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Wed, 21 Dec 2022 16:33:06 +0100
Subject: [PATCH] update in delayed_updating

+ couterexample to dbfr_ibfr when inner labels in b are not bound in b
---
 .../dbfr_unprotected_zero.ma}                 | 76 ++++++++++++++-----
 1 file changed, 58 insertions(+), 18 deletions(-)
 rename matita/matita/contribs/lambdadelta/delayed_updating/{etc/reduction/dbfr_unprotected.etc => reduction/dbfr_unprotected_zero.ma} (55%)

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/reduction/dbfr_unprotected.etc b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected_zero.ma
similarity index 55%
rename from matita/matita/contribs/lambdadelta/delayed_updating/etc/reduction/dbfr_unprotected.etc
rename to matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected_zero.ma
index 753d38c68..5b3631f9c 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/etc/reduction/dbfr_unprotected.etc
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected_zero.ma
@@ -23,26 +23,39 @@ include "ground/arith/pnat_two.ma".
 (* Example of unprotected balanced β-reduction ******************************)
 
 definition l3_t: prototerm ≝
-           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.⧣𝟏).
+           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).⧣𝟏).
 
 definition l3_i1: prototerm ≝
-           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛌.⧣𝟏).
+           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛌.⧣𝟏).
 
 definition l3_i2: prototerm ≝
-           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛌.⧣↑𝟐).
+           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛌.⧣↑𝟐).
+
+definition l3_i2': prototerm ≝
+           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛌.⧣↑↑𝟐).
 
 definition l3_d1: prototerm ≝
-           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛕𝟏.𝛌.⧣𝟏).
+           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛕𝟏.(𝛌.⧣𝟏)).
 
 definition l3_d2: prototerm ≝
-           (＠(⧣𝟏).＠(𝛌.⧣𝟏).𝛌.𝛕𝟏.𝛌.𝛕𝟏.⧣𝟏).
+           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛕𝟏.𝛌.(⧣𝟐)).
+
+definition l3_d2': prototerm ≝
+           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛕𝟏.𝛌.𝛕𝟏.(⧣𝟐)).
 
 lemma l3_ti1:
-      l3_t ➡𝐢𝐛𝐟[𝗔◗𝗔◗𝗟◗𝐞] l3_i1.
-@ibfr_appl_hd
-@ibfr_eq_trans [| @ibfr_beta_0 // ]
+      l3_t ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝐞] l3_i1.
+@ibfr_abst_hd
+@ibfr_eq_trans
+[ | @(ibfr_beta_0 … (𝟎))
+  [ /2 width=1 by pcc_A_sn, pcc_empty/
+  | >list_append_lcons_sn /2 width=1 by in_comp_appl_hd/
+  ]
+]
 @appl_eq_repl [ // ]
 @abst_eq_repl
+@(subset_eq_canc_sn … (fsubst_appl_hd …))
+@appl_eq_repl [ // ]
 @(subset_eq_canc_sn … (fsubst_empty_rc …))
 @(subset_eq_canc_sn … (lift_term_abst …))
 @abst_eq_repl
@@ -50,34 +63,61 @@ lemma l3_ti1:
 qed.
 
 lemma l3_i12:
-      l3_i1 ➡𝐢𝐛𝐟[𝗔◗𝗔◗𝗟◗𝗟◗𝐞] l3_i2.
-@ibfr_eq_trans [| @ibfr_beta_1 // ]
-@appl_eq_repl [ // ]
+      l3_i1 ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝗟◗𝐞] l3_i2.
+@ibfr_abst_hd
+@ibfr_appl_hd
+@ibfr_abst_hd
+@ibfr_eq_trans [| @ibfr_beta_0 // ]
 @appl_eq_repl [ // ]
 @abst_eq_repl
-@abst_eq_repl
 @(subset_eq_canc_sn … (fsubst_empty_rc …))
 @(subset_eq_canc_sn … (lift_term_oref_pap … )) //
 qed.
 
 lemma l3_td1:
-      l3_t ➡𝐝𝐛𝐟[𝗔◗𝗔◗𝗟◗𝐞] l3_d1.
-@dbfr_appl_hd
-@dbfr_eq_trans [| @dbfr_beta_0 // ]
+      l3_t ➡𝐝𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝐞] l3_d1.
+@dbfr_abst_hd
+@dbfr_eq_trans
+[ | @(dbfr_beta_0 … (𝟎))
+  [ /2 width=1 by pcc_A_sn, pcc_empty/
+  | >list_append_lcons_sn /2 width=1 by in_comp_appl_hd/
+  ]
+]
 @appl_eq_repl [ // ]
 @abst_eq_repl
-@(subset_eq_canc_sn … (fsubst_empty_rc …)) //
+@(subset_eq_canc_sn … (fsubst_appl_hd …))
+@appl_eq_repl [ // ]
+@(subset_eq_canc_sn … (fsubst_empty_rc …))
+@iref_eq_repl //
 qed.
 
-lemma ld_di2:
+lemma l3_di2:
       l3_i2 ⇔ ▼[𝐢]l3_d2.
+@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
 @(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
-[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) // ]
+[ @(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
+  @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
+]
+@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
+@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
+[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
+]
+@(subset_eq_canc_sn … (unwind2_term_iref …))
+@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
+@(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
+qed.
+
+lemma l3_di2':
+      l3_i2' ⇔ ▼[𝐢]l3_d2'.
+@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
 @(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
 [ @(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
   @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
 ]
 @(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
+@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
+[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
+]
 @(subset_eq_canc_sn … (unwind2_term_iref …))
 @(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
 @(subset_eq_canc_sn … (unwind2_term_iref …))
-- 
2.39.2