From 913070a2e9de2867b57e565c46800437a1c36104 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sat, 26 Mar 2022 21:12:19 +0100
Subject: [PATCH] update in delayed updating

+ additions to lift
---
 .../substitution/lift_constructors.ma         | 16 ++++++++-
 .../delayed_updating/substitution/lift_id.ma  | 30 +++++++++++++++++
 .../substitution/lift_prototerm_id.ma         | 33 +++++++++++++++++++
 .../delayed_updating/substitution/lift_uni.ma | 28 ++++++++++++++++
 4 files changed, 106 insertions(+), 1 deletion(-)
 create mode 100644 matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_id.ma
 create mode 100644 matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
 create mode 100644 matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_uni.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
index 31f4bbc14..772c837fb 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -12,11 +12,17 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_id.ma".
+include "delayed_updating/substitution/lift_uni.ma".
 include "delayed_updating/syntax/prototerm_constructors.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
 
+lemma lift_iref_bi (t1) (t2) (n):
+      t1 ⇔ t2 → 𝛗n.t1 ⇔ 𝛗n.t2.
+/2 width=1 by subset_equivalence_ext_f1_bi/
+qed.
+
 lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
       (𝛗f@❨n❩.↑[⇂*[n]f]t) ⊆ ↑[f](𝛗n.t).
 #f #t #n #p * #q * #r #Hr #H1 #H2 destruct
@@ -35,3 +41,11 @@ lemma lift_iref (f) (t) (n:pnat):
       (𝛗f@❨n❩.↑[⇂*[n]f]t) ⇔ ↑[f](𝛗n.t).
 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/
 qed.
+
+lemma lift_iref_uni (t) (m) (n):
+      (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).
+#t #m #n
+@(subset_eq_trans … (lift_iref …))
+<tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni
+/3 width=1 by lift_iref_bi, lift_term_id/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_id.ma
new file mode 100644
index 000000000..1d8b45295
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_id.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_eq.ma".
+include "ground/relocation/tr_id_pap.ma".
+include "ground/relocation/tr_id_tls.ma".
+
+(* LIFT FOR PATH ***********************************************************)
+
+(* Constructions with tr_id ************************************************)
+
+lemma lift_path_id (p):
+      p = ↑[𝐢]p.
+#p elim p -p //
+* [ #n ] #p #IH //
+[ <lift_path_d_sn //
+| <lift_path_L_sn //
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
new file mode 100644
index 000000000..cc7569284
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
@@ -0,0 +1,33 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_prototerm_eq.ma".
+include "delayed_updating/substitution/lift_id.ma".
+
+lemma lift_term_id_sn (t):
+      t ⊆ ↑[𝐢]t.
+#t #p #Hp
+>(lift_path_id p)
+/2 width=1 by in_comp_lift_bi/
+qed-.
+
+lemma lift_term_id_dx (t):
+      ↑[𝐢]t ⊆ t.
+#t #p * #q #Hq #H destruct //
+qed-.
+
+lemma lift_term_id (t):
+      t ⇔ ↑[𝐢]t.
+/3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/      
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_uni.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_uni.ma
new file mode 100644
index 000000000..cd6c79533
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_uni.ma
@@ -0,0 +1,28 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_id.ma".
+include "ground/relocation/tr_uni_pap.ma".
+include "ground/relocation/tr_uni_tls.ma".
+
+(* LIFT FOR PATH ***********************************************************)
+
+(* Constructions with tr_uni ***********************************************)
+
+lemma lift_path_d_sn_uni (p) (m) (n):
+      (𝗱(n+m)◗p) = ↑[𝐮❨m❩](𝗱(n)◗p).
+#p #m #n
+<lift_path_d_sn <tr_uni_pap >nsucc_pnpred
+<tr_tls_succ_uni //
+qed.
-- 
2.39.2