From: Ferruccio Guidi <fguidi@maelstrom.helm.cs.unibo.it>
Date: Wed, 27 Apr 2022 17:24:30 +0000 (+0200)
Subject: update un delayed updating
X-Git-Tag: make_still_working~76^2~5
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=e6482f7f499fbb88aff8a205d2a2c808158042c5;p=helm.git
update un delayed updating
+ some parked files
---
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap.etc
new file mode 100644
index 000000000..c35244d88
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap.etc
@@ -0,0 +1,48 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground/arith/pnat_plus.ma".
+include "ground/relocation/tr_map.ma".
+include "delayed_updating/notation/functions/verticalbarat_2.ma".
+
+(* POSITIVE APPLICATION FOR STACKS OF BASIC RELOCATION MAPS *****************)
+
+rec definition sbr_pap (i: pnat) on i: tr_map â pnat.
+* #p #f cases i -i
+[ @(p)
+| #i cases p -p
+ [ lapply (sbr_pap i f) -sbr_pap -i -f
+ #i @(âi)
+ | #p @(i+âp)
+ ]
+]
+defined.
+
+interpretation
+ "functional positive application (stack of relocation maps)"
+ 'VerticalBarAt f i = (sbr_pap i f).
+
+(* Basic constructions ******************************************************)
+
+lemma sbr_pap_unfold_unit (f):
+ âp. p = (p⨮f)â@â¨ðâ©.
+// qed.
+
+lemma sbr_pap_unfold_unit_succ (f):
+ âi. â(fâ@â¨iâ©) = (ð⨮f)â@â¨âiâ©.
+// qed.
+
+lemma sbr_pap_unfold_succ_bi (f):
+ âp,i. i+âp = (âp⨮f)â@â¨âiâ©.
+// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_eq.etc
new file mode 100644
index 000000000..10b0d939e
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_eq.etc
@@ -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/relocation/sbr_pap.ma".
+include "ground/relocation/tr_eq.ma".
+
+(* POSITIVE APPLICATION FOR STACKS OF BASIC RELOCATION MAPS *****************)
+
+(* Main constructions with stream_eq ****************************************)
+
+theorem sbr_pap_eq_repl_sn (i):
+ stream_eq_repl ⦠(λf1,f2. f1â@â¨iâ© = f2â@â¨iâ©).
+#i elim i -i [| #i #IH ]
+* [ #p1 | * [| #p1 ]] #f1
+* #p2 #f2 #H
+elim (stream_eq_inv_cons_bi ⦠H) -H [1,8,15: |*: // ] #Hp #Hf destruct //
+<sbr_pap_unfold_unit_succ <sbr_pap_unfold_unit_succ
+/3 width=1 by eq_f/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_id.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_id.etc
new file mode 100644
index 000000000..b7e30698a
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_id.etc
@@ -0,0 +1,26 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/relocation/sbr_pap.ma".
+include "ground/relocation/tr_id.ma".
+
+(* POSITIVE APPLICATION FOR STACKS OF BASIC RELOCATION MAPS *****************)
+
+(* Constructions with tr_id *************************************************)
+
+lemma sbr_pap_id (p):
+ p = ð¢â@â¨pâ©.
+#p elim p -p [| #p #IH ] <tr_id_unfold //
+<sbr_pap_unfold_unit_succ //
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_push.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_push.etc
new file mode 100644
index 000000000..bd2988e85
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_pap_push.etc
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/relocation/sbr_pap.ma".
+include "delayed_updating/relocation/sbr_push.ma".
+
+(* POSITIVE APPLICATION FOR BASIC STACKS OF RELOCATION MAPS *****************)
+
+(* constructions with sbr_push **********************************************)
+
+lemma sbr_push_pap_unit (f) (p):
+ âp = (p⫯âf)â@â¨ðâ©.
+// qed.
+
+lemma sbr_push_pap (f) (q) (p):
+ q + p = (p⫯âf)â@â¨qâ©.
+#f * //
+#q * //
+#p <sbr_pap_unfold_succ_bi //
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push.etc
new file mode 100644
index 000000000..e1329185e
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push.etc
@@ -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 "ground/relocation/tr_map.ma".
+include "delayed_updating/notation/functions/upspoonverticalbar_2.ma".
+
+(* PUSH FOR STACKS OF BASIC RELOCATION MAPS *********************************)
+
+definition sbr_push (p:pnat) (f): tr_map â (âp)⨮f.
+
+interpretation
+ "push (stack of basic relocation maps)"
+ 'UpSpoonVerticalBar n f = (sbr_push n f).
+
+(* Basic properties *********************************************************)
+
+lemma sbr_push_unfold (p) (f):
+ (âp)⨮f = p⫯âf.
+// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push_eq.etc
new file mode 100644
index 000000000..65c9d387b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push_eq.etc
@@ -0,0 +1,24 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/relocation/sbr_push.ma".
+include "ground/relocation/tr_eq.ma".
+
+(* PUSH FOR STACKS OF BASIC RELOCATION MAPS *********************************)
+
+(* Main constructions with stream_eq ****************************************)
+
+theorem sbr_push_eq_repl_dx (p):
+ stream_eq_repl ⦠(λf1,f2. p⫯âf1 â p⫯âf2).
+/2 width=1 by stream_eq_cons/ qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push_uni.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push_uni.etc
new file mode 100644
index 000000000..edfd82efd
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/sbr_push_uni.etc
@@ -0,0 +1,24 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/relocation/sbr_push.ma".
+include "ground/relocation/tr_uni.ma".
+
+(* PUSH FOR STACKS OF BASIC RELOCATION MAPS *********************************)
+
+(* Constructions with tr_uni ************************************************)
+
+theorem sbr_push_id (p:pnat):
+ (ð®â¨pâ©) = p⫯âð¢.
+// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/upspoonverticalbar_2.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/upspoonverticalbar_2.etc
new file mode 100644
index 000000000..4b4866516
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/upspoonverticalbar_2.etc
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+(* GROUND NOTATION **********************************************************)
+
+notation "hvbox( hd ⫯â break tl )"
+ right associative with precedence 47
+ for @{ 'UpSpoonVerticalBar $hd $tl }.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/verticalbarat_2.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/verticalbarat_2.etc
new file mode 100644
index 000000000..ce7cd1410
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/relocation/verticalbarat_2.etc
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR DELAYED UPDATING ********************************************)
+
+notation "hvbox( f â@⨠break term 46 a â© )"
+ non associative with precedence 60
+ for @{ 'VerticalBarAt $f $a }.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind.etc
new file mode 100644
index 000000000..1713625e8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind.etc
@@ -0,0 +1,189 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground/relocation/tr_compose_pap.ma".
+include "ground/relocation/tr_uni_pap.ma".
+include "delayed_updating/syntax/path.ma".
+include "delayed_updating/notation/functions/black_downtriangle_4.ma".
+include "delayed_updating/notation/functions/black_downtriangle_2.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+definition unwind_continuation (A:Type[0]) â
+tr_map â path â A.
+
+rec definition unwind_gen (A:Type[0]) (k:unwind_continuation A) (f) (p) on p â
+match p with
+[ list_empty â k f (ð)
+| list_lcons l q â
+ match l with
+ [ label_d n â
+ match q with
+ [ list_empty â unwind_gen (A) (λg,p. k g (ð±(f@â¨nâ©)âp)) (fâð®â¨nâ©) q
+ | list_lcons _ _ â unwind_gen (A) k (fâð®â¨nâ©) q
+ ]
+ | label_m â unwind_gen (A) k f q
+ | label_L â unwind_gen (A) (λg,p. k g (ðâp)) (⫯f) q
+ | label_A â unwind_gen (A) (λg,p. k g (ðâp)) f q
+ | label_S â unwind_gen (A) (λg,p. k g (ð¦âp)) f q
+ ]
+].
+
+interpretation
+ "unwind (gneric)"
+ 'BlackDownTriangle A k f p = (unwind_gen A k f p).
+
+definition proj_path: unwind_continuation ⦠â
+ λf,p.p.
+
+definition proj_rmap: unwind_continuation ⦠â
+ λf,p.f.
+
+interpretation
+ "unwind (path)"
+ 'BlackDownTriangle f p = (unwind_gen ? proj_path f p).
+
+interpretation
+ "unwind (relocation map)"
+ 'BlackDownTriangle p f = (unwind_gen ? proj_rmap f p).
+
+(* Basic constructions ******************************************************)
+
+lemma unwind_empty (A) (k) (f):
+ k f (ð) = â¼{A}â¨k, f, ðâ©.
+// qed.
+
+lemma unwind_d_empty_sn (A) (k) (n) (f):
+ â¼â¨(λg,p. k g (ð±(f@â¨nâ©)âp)), fâð®â¨ninj nâ©, ðâ© = â¼{A}â¨k, f,
+ð±nâðâ©.
+// qed.
+
+lemma unwind_d_lcons_sn (A) (k) (p) (l) (n) (f):
+ â¼â¨k, fâð®â¨ninj nâ©, lâpâ© = â¼{A}â¨k, f, ð±nâlâpâ©.
+// qed.
+
+lemma unwind_m_sn (A) (k) (p) (f):
+ â¼â¨k, f, pâ© = â¼{A}â¨k, f, ðºâpâ©.
+// qed.
+
+lemma unwind_L_sn (A) (k) (p) (f):
+ â¼â¨(λg,p. k g (ðâp)), ⫯f, pâ© = â¼{A}â¨k, f, ðâpâ©.
+// qed.
+
+lemma unwind_A_sn (A) (k) (p) (f):
+ â¼â¨(λg,p. k g (ðâp)), f, pâ© = â¼{A}â¨k, f, ðâpâ©.
+// qed.
+
+lemma unwind_S_sn (A) (k) (p) (f):
+ â¼â¨(λg,p. k g (ð¦âp)), f, pâ© = â¼{A}â¨k, f, ð¦âpâ©.
+// qed.
+
+(* Basic constructions with proj_path ***************************************)
+
+lemma unwind_path_empty (f):
+ (ð) = â¼[f]ð.
+// qed.
+
+lemma unwind_path_d_empty_sn (f) (n):
+ ð±(f@â¨nâ©)âð = â¼[f](ð±nâð).
+// qed.
+
+lemma unwind_path_d_lcons_sn (f) (p) (l) (n):
+ â¼[fâð®â¨ninj nâ©](lâp) = â¼[f](ð±nâlâp).
+// qed.
+
+lemma unwind_path_m_sn (f) (p):
+ â¼[f]p = â¼[f](ðºâp).
+// qed.
+
+(* Basic constructions with proj_rmap ***************************************)
+
+lemma unwind_rmap_empty (f):
+ f = â¼[ð]f.
+// qed.
+
+lemma unwind_rmap_d_sn (f) (p) (n):
+ â¼[p](fâð®â¨ninj nâ©) = â¼[ð±nâp]f.
+#f * // qed.
+
+lemma unwind_rmap_m_sn (f) (p):
+ â¼[p]f = â¼[ðºâp]f.
+// qed.
+
+lemma unwind_rmap_L_sn (f) (p):
+ â¼[p](⫯f) = â¼[ðâp]f.
+// qed.
+
+lemma unwind_rmap_A_sn (f) (p):
+ â¼[p]f = â¼[ðâp]f.
+// qed.
+
+lemma unwind_rmap_S_sn (f) (p):
+ â¼[p]f = â¼[ð¦âp]f.
+// qed.
+
+(* Advanced constructions with proj_rmap and path_append ********************)
+
+lemma unwind_rmap_append (p2) (p1) (f):
+ â¼[p2]â¼[p1]f = â¼[p1âp2]f.
+#p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
+[ <unwind_rmap_m_sn <unwind_rmap_m_sn //
+| <unwind_rmap_A_sn <unwind_rmap_A_sn //
+| <unwind_rmap_S_sn <unwind_rmap_S_sn //
+]
+qed.
+
+(* Advanced constructions with proj_rmap and path_rcons *********************)
+
+lemma unwind_rmap_d_dx (f) (p) (n):
+ (â¼[p]f)âð®â¨ninj nâ© = â¼[pâð±n]f.
+// qed.
+
+lemma unwind_rmap_m_dx (f) (p):
+ â¼[p]f = â¼[pâðº]f.
+// qed.
+
+lemma unwind_rmap_L_dx (f) (p):
+ (⫯â¼[p]f) = â¼[pâð]f.
+// qed.
+
+lemma unwind_rmap_A_dx (f) (p):
+ â¼[p]f = â¼[pâð]f.
+// qed.
+
+lemma unwind_rmap_S_dx (f) (p):
+â¼[p]f = â¼[pâð¦]f.
+// qed.
+
+lemma unwind_rmap_pap_d_dx (f) (p) (n) (m):
+ â¼[p]f@â¨m+nâ© = â¼[pâð±n]f@â¨mâ©.
+#f #p #n #m
+<unwind_rmap_d_dx <tr_compose_pap <tr_uni_pap //
+qed.
+
+(* Advanced eliminations with path ******************************************)
+
+lemma path_ind_unwind (Q:predicate â¦):
+ Q (ð) â
+ (ân. Q (ð) â Q (ð±nâð)) â
+ (ân,l,p. Q (lâp) â Q (ð±nâlâp)) â
+ (âp. Q p â Q (ðºâp)) â
+ (âp. Q p â Q (ðâp)) â
+ (âp. Q p â Q (ðâp)) â
+ (âp. Q p â Q (ð¦âp)) â
+ âp. Q p.
+#Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #p
+elim p -p [| * [ #n * ] ]
+/2 width=1 by/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_constructors.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_constructors.etc
new file mode 100644
index 000000000..93ddb2ef6
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_constructors.etc
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind2/unwind_prototerm_eq.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+lemma unwind_iref_after_sn (f) (t:prototerm) (n:pnat):
+ â¼[fâð®â¨nâ©]t â â¼[f](ðn.t).
+#f #t #n #p * #q #Hq #H0 destruct
+@(ex2_intro ⦠(ð±nâðºâq))
+/2 width=1 by in_comp_iref/
+qed-.
+
+lemma unwind_iref_after_dx (f) (t) (n:pnat):
+ â¼[f](ðn.t) â â¼[fâð®â¨nâ©]t.
+#f #t #n #p * #q #Hq #H0 destruct
+elim (in_comp_inv_iref ⦠Hq) -Hq #p #Hp #Ht destruct
+/2 width=1 by in_comp_unwind_bi/
+qed-.
+
+lemma unwind_iref_after (f) (t) (n:pnat):
+ â¼[fâð®â¨nâ©]t â â¼[f](ðn.t).
+/3 width=1 by conj, unwind_iref_after_sn, unwind_iref_after_dx/
+qed.
+
+lemma unwind_iref (f) (t) (n:pnat):
+ â¼[f]â¼[ð®â¨nâ©]t â â¼[f](ðn.t).
+/3 width=3 by unwind_term_after, subset_eq_trans/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_depth.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_depth.etc
new file mode 100644
index 000000000..8715fb514
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_depth.etc
@@ -0,0 +1,48 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind2/unwind.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/relocation/tr_id_compose.ma".
+include "ground/relocation/tr_compose_compose.ma".
+include "ground/relocation/tr_compose_pn.ma".
+include "ground/relocation/tr_compose_eq.ma".
+include "ground/relocation/tr_pn_eq.ma".
+include "ground/lib/stream_eq_eq.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+(* Constructions with depth *************************************************)
+
+lemma unwind_rmap_decompose (p) (f):
+ â¼[p]f â (⫯*[âpâ]f)â(â¼[p]ð¢).
+#p @(list_ind_rcons ⦠p) -p
+[ #f <unwind_rmap_empty <unwind_rmap_empty <tr_pushs_zero //
+| #p * [ #n ] #IH #f //
+ [ <unwind_rmap_d_dx <unwind_rmap_d_dx <depth_d_dx
+ @(stream_eq_trans ⦠(tr_compose_assoc â¦))
+ /2 width=1 by tr_compose_eq_repl/
+ | <unwind_rmap_L_dx <unwind_rmap_L_dx <depth_L_dx
+ <tr_pushs_succ <tr_compose_push_bi
+ /2 width=1 by tr_push_eq_repl/
+ ]
+]
+qed.
+
+lemma unwind_rmap_pap_le (f) (p) (n):
+ (â¼[p]ð¢)@â¨nâ© < ââpâ â (â¼[p]ð¢)@â¨nâ© = (â¼[p]f)@â¨nâ©.
+#f #p #n #Hn
+>(tr_pap_eq_repl ⦠(â¼[p]f) ⦠(unwind_rmap_decompose â¦))
+<tr_compose_pap @tr_pap_pushs_le //
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_eq.etc
new file mode 100644
index 000000000..b3c0b40e3
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_eq.etc
@@ -0,0 +1,122 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind2/unwind.ma".
+include "ground/relocation/tr_uni_compose.ma".
+include "ground/relocation/tr_compose_compose.ma".
+include "ground/relocation/tr_compose_eq.ma".
+include "ground/relocation/tr_pn_eq.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+definition unwind_exteq (A): relation2 (unwind_continuation A) (unwind_continuation A) â
+ λk1,k2. âf1,f2,p. f1 â f2 â k1 f1 p = k2 f2 p.
+
+interpretation
+ "extensional equivalence (unwind continuation)"
+ 'RingEq A k1 k2 = (unwind_exteq A k1 k2).
+
+(* Constructions with unwind_exteq ******************************************)
+
+lemma unwind_eq_repl (A) (p) (k1) (k2):
+ k1 â{A} k2 â stream_eq_repl ⦠(λf1,f2. â¼â¨k1, f1, pâ© = â¼â¨k2, f2, pâ©).
+#A #p @(path_ind_unwind ⦠p) -p [| #n #IH | #n #l0 #q #IH |*: #q #IH ]
+#k1 #k2 #Hk #f1 #f2 #Hf
+[ <unwind_empty <unwind_empty /2 width=1 by/
+| <unwind_d_empty_sn <unwind_d_empty_sn <(tr_pap_eq_repl ⦠Hf)
+ /3 width=1 by tr_compose_eq_repl, stream_eq_refl/
+| <unwind_d_lcons_sn <unwind_d_lcons_sn
+ /3 width=1 by tr_compose_eq_repl, stream_eq_refl/
+| /2 width=1 by/
+| /3 width=1 by tr_push_eq_repl/
+| /3 width=1 by/
+| /3 width=1 by/
+]
+qed-.
+
+(* Advanced constructions ***************************************************)
+
+lemma unwind_lcons_alt (A) (k) (f) (p) (l): k â k â
+ â¼â¨Î»g,p2. k g (lâp2), f, pâ© = â¼{A}â¨Î»g,p2. k g ((lâð)âp2), f, pâ©.
+#A #k #f #p #l #Hk
+@unwind_eq_repl // #g1 #g2 #p2 #Hg @Hk -Hk // (**) (* auto fail *)
+qed.
+
+lemma unwind_append_rcons_sn (A) (k) (f) (p1) (p) (l): k â k â
+ â¼â¨Î»g,p2. k g (p1âlâp2), f, pâ© = â¼{A}â¨Î»g,p2. k g (p1âlâp2), f, pâ©.
+#A #k #f #p1 #p #l #Hk
+@unwind_eq_repl // #g1 #g2 #p2 #Hg
+<list_append_rcons_sn @Hk -Hk // (**) (* auto fail *)
+qed.
+
+(* Advanced constructions with proj_path ************************************)
+
+lemma proj_path_proper:
+ proj_path â proj_path.
+// qed.
+
+lemma unwind_path_eq_repl (p):
+ stream_eq_repl ⦠(λf1,f2. â¼[f1]p = â¼[f2]p).
+/2 width=1 by unwind_eq_repl/ qed.
+
+lemma unwind_path_append_sn (p) (f) (q):
+ qââ¼[f]p = â¼â¨(λg,p. proj_path g (qâp)), f, pâ©.
+#p @(path_ind_unwind ⦠p) -p // [ #n #l #p |*: #p ] #IH #f #q
+[ <unwind_d_lcons_sn <unwind_d_lcons_sn <IH -IH //
+| <unwind_m_sn <unwind_m_sn //
+| <unwind_L_sn <unwind_L_sn >unwind_lcons_alt // >unwind_append_rcons_sn //
+ <IH <IH -IH <list_append_rcons_sn //
+| <unwind_A_sn <unwind_A_sn >unwind_lcons_alt >unwind_append_rcons_sn //
+ <IH <IH -IH <list_append_rcons_sn //
+| <unwind_S_sn <unwind_S_sn >unwind_lcons_alt >unwind_append_rcons_sn //
+ <IH <IH -IH <list_append_rcons_sn //
+]
+qed.
+
+lemma unwind_path_lcons (f) (p) (l):
+ lââ¼[f]p = â¼â¨(λg,p. proj_path g (lâp)), f, pâ©.
+#f #p #l
+>unwind_lcons_alt <unwind_path_append_sn //
+qed.
+
+lemma unwind_path_L_sn (f) (p):
+ (ðââ¼[⫯f]p) = â¼[f](ðâp).
+// qed.
+
+lemma unwind_path_A_sn (f) (p):
+ (ðââ¼[f]p) = â¼[f](ðâp).
+// qed.
+
+lemma unwind_path_S_sn (f) (p):
+ (ð¦ââ¼[f]p) = â¼[f](ð¦âp).
+// qed.
+
+lemma unwind_path_after (p) (f1) (f2):
+ â¼[f2]â¼[f1]p = â¼[f2âf1]p.
+#p @(path_ind_unwind ⦠p) -p // [ #n #l #p | #p ] #IH #f1 #f2
+[ <unwind_path_d_lcons_sn <unwind_path_d_lcons_sn
+ >(unwind_path_eq_repl ⦠(tr_compose_assoc â¦)) //
+| <unwind_path_L_sn <unwind_path_L_sn <unwind_path_L_sn
+ >tr_compose_push_bi //
+]
+qed.
+
+(* Advanced constructions with proj_rmap and stream_tls *********************)
+
+lemma unwind_rmap_tls_d_dx (f) (p) (m) (n):
+ â*[m+n]â¼[p]f â â*[m]â¼[pâð±n]f.
+#f #p #m #n
+<unwind_rmap_d_dx >nrplus_inj_dx
+/2 width=1 by tr_tls_compose_uni_dx/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_etc.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_etc.etc
new file mode 100644
index 000000000..a9e563db6
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_etc.etc
@@ -0,0 +1,10 @@
+include "delayed_updating/unwind2/unwind_depth.ma".
+include "ground/relocation/tr_uni_compose.ma".
+
+lemma pippo (q) (p):
+ â¼[p]ð¢ â â*[ââqâ]â¼[pâðâq]ð¢.
+#q @(list_ind_rcons ⦠q) -q //
+#q * [ #n ] #IH #p //
+<depth_d_dx >list_cons_shift <list_append_assoc
+<unwind_rmap_d_dx
+check tr_tls_compose_uni_sn
\ No newline at end of file
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_fsubst.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_fsubst.etc
new file mode 100644
index 000000000..fedc665fb
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_fsubst.etc
@@ -0,0 +1,61 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind2/unwind_prototerm_eq.ma".
+include "delayed_updating/unwind2/unwind_structure.ma".
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/syntax/preterm.ma".
+include "delayed_updating/syntax/prototerm_proper.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+(* Constructions with fsubst ************************************************)
+
+lemma unwind_fsubst_sn (f) (t) (u) (p): u ϵ ð â
+ (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u] â â¼[f](t[âpâu]).
+#f #t #u #p #Hu #ql * *
+[ #rl * #r #Hr #H1 #H2 destruct
+ >unwind_append_proper_dx
+ /4 width=5 by in_comp_unwind_bi, in_ppc_comp_trans, or_introl, ex2_intro/
+| * #q #Hq #H1 #H0
+ @(ex2_intro ⦠H1) @or_intror @conj // *
+ [ <list_append_empty_dx #H2 destruct
+ elim (unwind_path_root f q) #r #_ #Hr /2 width=2 by/
+ | #l #r #H2 destruct
+ @H0 -H0 [| <unwind_append_proper_dx /2 width=3 by ppc_lcons/ ]
+ ]
+]
+qed-.
+
+lemma unwind_fsubst_dx (f) (t) (u) (p): u ϵ ð â p ϵ âµt â t ϵ ð â
+ â¼[f](t[âpâu]) â (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u].
+#f #t #u #p #Hu #H1p #H2p #ql * #q * *
+[ #r #Hu #H1 #H2 destruct
+ @or_introl @ex2_intro
+ [|| <unwind_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
+ /2 width=3 by ex2_intro/
+| #Hq #H0 #H1 destruct
+ @or_intror @conj [ /2 width=1 by in_comp_unwind_bi/ ] *
+ [ <list_append_empty_dx #Hr @(H0 ⦠(ð)) -H0
+ <list_append_empty_dx @H2p -H2p /2 width=1 by prototerm_in_comp_root/
+ | #l #r #Hr
+ elim (unwind_inv_append_proper_dx ⦠Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
+ lapply (H2p ⦠Hs1) -H2p -Hs1 /2 width=2 by ex_intro/
+ ]
+]
+qed-.
+
+lemma unwind_fsubst (f) (t) (u) (p): u ϵ ð â p ϵ âµt â t ϵ ð â
+ (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u] â â¼[f](t[âpâu]).
+/4 width=3 by unwind_fsubst_sn, conj, unwind_fsubst_dx/ qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_height.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_height.etc
new file mode 100644
index 000000000..d2678f61e
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_height.etc
@@ -0,0 +1,83 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind2/unwind_eq.ma".
+include "delayed_updating/syntax/path_height.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/lib/stream_eq_eq.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+(* Constructions with height ************************************************)
+
+lemma unwind_rmap_pap_le (f1) (f2) (p) (m:pnat) (l:nat):
+ ninj (m+⧣p+l) = âpâ â
+ (â¼[p]f1)@â¨mâ© = (â¼[p]f2)@â¨mâ©.
+#f1 #f2 #p @(list_ind_rcons ⦠p) -p
+[ #m #l <depth_empty #H0 destruct
+| #p * [ #n ] #IH #m #l
+ [ <height_d_dx <depth_d_dx <unwind_rmap_pap_d_dx <unwind_rmap_pap_d_dx
+ <nplus_comm <nrplus_inj_sn <nrplus_inj_dx <nrplus_pplus_assoc
+ #H0 <(IH ⦠l) -IH //
+ | /2 width=2 by/
+ | <height_L_dx <depth_L_dx <unwind_rmap_L_dx <unwind_rmap_L_dx
+ cases m -m // #m
+ <nrplus_succ_sn <nrplus_succ_sn >nsucc_inj #H0
+ <tr_pap_push <tr_pap_push
+ <(IH ⦠l) -IH //
+ | /2 width=2 by/
+ | /2 width=2 by/
+ ]
+]
+qed.
+
+lemma unwind_rmap_pap_gt (f) (p) (m):
+ f@â¨m+⧣pâ©+âpâ = (â¼[p]f)@â¨m+âpââ©.
+#f #p @(list_ind_rcons ⦠p) -p [ // ]
+#p * [ #n ] #IH #m
+[ <height_d_dx <depth_d_dx
+ <nplus_comm <nrplus_inj_sn <nrplus_inj_dx <nrplus_pplus_assoc
+ <unwind_rmap_pap_d_dx >IH -IH //
+| //
+| <height_L_dx <depth_L_dx
+ <nrplus_succ_dx <nrplus_succ_dx <unwind_rmap_L_dx <tr_pap_push //
+| //
+| //
+]
+qed.
+
+lemma unwind_rmap_tls_gt (f) (p) (m:pnat):
+ â*[ninj (m+⧣p)]f â â*[ninj (m+âpâ)]â¼[p]f.
+#f #p @(list_ind_rcons ⦠p) -p [ // ]
+#p * [ #n ] #IH #m
+[ <height_d_dx <depth_d_dx
+ <nplus_comm <nrplus_inj_sn <nrplus_inj_dx <nrplus_pplus_assoc
+ @(stream_eq_trans ⦠(unwind_rmap_tls_d_dx â¦))
+ @(stream_eq_canc_dx ⦠(IH â¦)) -IH //
+| //
+| <height_L_dx <depth_L_dx
+ <nrplus_succ_dx >nsucc_inj //
+| //
+| //
+]
+qed.
+
+lemma unwind_rmap_tls_eq (f) (p):
+ â*[⧣p]f â â*[ââpâ]â¼[p]⫯f.
+(*
+#f #p @(list_ind_rcons ⦠p) -p //
+#p * [ #n ] #IH //
+<height_d_dx <depth_d_dx <unwind_rmap_d_dx
+@(stream_eq_trans ⦠(tr_tls_compose_uni_dx â¦))
+*)
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_preterm_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_preterm_eq.etc
new file mode 100644
index 000000000..d60c54cc6
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_preterm_eq.etc
@@ -0,0 +1,68 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground/lib/subset_equivalence.ma".
+include "delayed_updating/syntax/path_structure_inner.ma".
+include "delayed_updating/syntax/preterm.ma".
+include "delayed_updating/unwind2/unwind_structure.ma".
+include "delayed_updating/unwind2/unwind_prototerm.ma".
+
+(* UNWIND FOR PRETERM *******************************************************)
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma unwind_grafted_sn (f) (t) (p): p ϵ ð â
+ â¼[â¼[p]f](tâp) â (â¼[f]t)â(âp).
+#f #t #p #Hp #q * #r #Hr #H0 destruct
+@(ex2_intro ⦠Hr) -Hr
+<unwind_append_inner_sn //
+qed-.
+
+lemma unwind_grafted_dx (f) (t) (p): p ϵ ð â p ϵ âµt â t ϵ ð â
+ (â¼[f]t)â(âp) â â¼[â¼[p]f](tâp).
+#f #t #p #H1p #H2p #Ht #q * #r #Hr #H0
+elim (unwind_inv_append_inner_sn ⦠(sym_eq ⦠H0)) -H0 //
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+<(Ht ⦠Hp0) [|*: /2 width=2 by ex_intro/ ] -p
+/2 width=1 by in_comp_unwind_bi/
+qed-.
+
+lemma unwind_grafted (f) (t) (p): p ϵ ð â p ϵ âµt â t ϵ ð â
+ â¼[â¼[p]f](tâp) â (â¼[f]t)â(âp).
+/3 width=1 by unwind_grafted_sn, conj, unwind_grafted_dx/ qed.
+
+
+lemma unwind_grafted_S_dx (f) (t) (p): p ϵ âµt â t ϵ ð â
+ (â¼[f]t)â((âp)âð¦) â â¼[â¼[p]f](tâ(pâð¦)).
+#f #t #p #Hp #Ht #q * #r #Hr
+<list_append_rcons_sn #H0
+elim (unwind_inv_append_proper_dx ⦠(sym_eq ⦠H0)) -H0 //
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+<(Ht ⦠Hp0) [|*: /2 width=2 by ex_intro/ ] -p
+elim (unwind_path_inv_S_sn ⦠(sym_eq ⦠Hq0)) -Hq0
+#r1 #r2 #Hr1 #Hr2 #H0 destruct
+lapply (preterm_in_root_append_inv_structure_empty_dx ⦠p0 ⦠Ht Hr1)
+[ /2 width=2 by ex_intro/ ] -Hr1 #Hr1 destruct
+/2 width=1 by in_comp_unwind_bi/
+qed-.
+
+lemma unwind_grafted_S (f) (t) (p): p ϵ âµt â t ϵ ð â
+ â¼[â¼[p]f](tâ(pâð¦)) â (â¼[f]t)â((âp)âð¦).
+#f #t #p #Hp #Ht
+@conj
+[ >unwind_rmap_S_dx >structure_S_dx
+ @unwind_grafted_sn //
+| /2 width=1 by unwind_grafted_S_dx/
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_prototerm.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_prototerm.etc
new file mode 100644
index 000000000..1a5d46b77
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_prototerm.etc
@@ -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/unwind2/unwind.ma".
+include "delayed_updating/syntax/prototerm.ma".
+include "ground/lib/subset_ext.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+interpretation
+ "unwind (prototerm)"
+ 'BlackDownTriangle f t = (subset_ext_f1 ? ? (unwind_gen ? proj_path f) t).
+
+(* Basic constructions ******************************************************)
+
+lemma in_comp_unwind_bi (f) (p) (t):
+ p ϵ t â â¼[f]p ϵ â¼[f]t.
+/2 width=1 by subset_in_ext_f1_dx/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_prototerm_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_prototerm_eq.etc
new file mode 100644
index 000000000..15b8cdb2c
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_prototerm_eq.etc
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground/lib/subset_ext_equivalence.ma".
+include "delayed_updating/unwind2/unwind_eq.ma".
+include "delayed_updating/unwind2/unwind_prototerm.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma unwind_term_eq_repl_sn (f1) (f2) (t):
+ f1 â f2 â â¼[f1]t â â¼[f2]t.
+/3 width=1 by subset_equivalence_ext_f1_exteq, unwind_path_eq_repl/
+qed.
+
+lemma unwind_term_eq_repl_dx (f) (t1) (t2):
+ t1 â t2 â â¼[f]t1 â â¼[f]t2.
+/2 width=1 by subset_equivalence_ext_f1_bi/
+qed.
+
+lemma unwind_term_after (f1) (f2) (t):
+ â¼[f2]â¼[f1]t â â¼[f2âf1]t.
+#f1 #f2 #t @subset_eq_trans
+[
+| @subset_inclusion_ext_f1_compose
+| @subset_equivalence_ext_f1_exteq /2 width=5/
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_structure.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_structure.etc
new file mode 100644
index 000000000..b5d92a577
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_structure.etc
@@ -0,0 +1,269 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind2/unwind_eq.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_inner.ma".
+include "delayed_updating/syntax/path_proper.ma".
+include "ground/xoa/ex_4_2.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+(* Basic constructions with structure ***************************************)
+
+lemma structure_unwind (p) (f):
+ âp = ââ¼[f]p.
+#p @(path_ind_unwind ⦠p) -p // #p #IH #f
+<unwind_path_L_sn //
+qed.
+
+lemma unwind_structure (p) (f):
+ âp = â¼[f]âp.
+#p @(path_ind_unwind ⦠p) -p //
+qed.
+
+(* Destructions with structure **********************************************)
+
+lemma unwind_des_structure (q) (p) (f):
+ âq = â¼[f]p â âq = âp.
+// qed-.
+
+(* Constructions with proper condition for path *****************************)
+
+lemma unwind_append_proper_dx (p2) (p1) (f): p2 ϵ ð â
+ (âp1)â(â¼[â¼[p1]f]p2) = â¼[f](p1âp2).
+#p2 #p1 @(path_ind_unwind ⦠p1) -p1 //
+[ #n | #n #l #p1 |*: #p1 ] #IH #f #Hp2
+[ elim (ppc_inv_lcons ⦠Hp2) -Hp2 #l #q #H destruct //
+| <unwind_path_d_lcons_sn <IH //
+| <unwind_path_m_sn <IH //
+| <unwind_path_L_sn <IH //
+| <unwind_path_A_sn <IH //
+| <unwind_path_S_sn <IH //
+]
+qed-.
+
+(* Constructions with inner condition for path ******************************)
+
+lemma unwind_append_inner_sn (p1) (p2) (f): p1 ϵ ð â
+ (âp1)â(â¼[â¼[p1]f]p2) = â¼[f](p1âp2).
+#p1 @(list_ind_rcons ⦠p1) -p1 // #p1 *
+[ #n ] #_ #p2 #f #Hp1
+[ elim (pic_inv_d_dx ⦠Hp1)
+| <list_append_rcons_sn <unwind_append_proper_dx //
+| <list_append_rcons_sn <unwind_append_proper_dx //
+ <structure_L_dx <list_append_rcons_sn //
+| <list_append_rcons_sn <unwind_append_proper_dx //
+ <structure_A_dx <list_append_rcons_sn //
+| <list_append_rcons_sn <unwind_append_proper_dx //
+ <structure_S_dx <list_append_rcons_sn //
+]
+qed-.
+
+(* Advanced constructions with proj_path ************************************)
+
+lemma unwind_path_d_empty_dx (n) (p) (f):
+ (âp)âð±((â¼[p]f)@â¨nâ©) = â¼[f](pâð±n).
+#n #p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_m_dx (p) (f):
+ âp = â¼[f](pâðº).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_L_dx (p) (f):
+ (âp)âð = â¼[f](pâð).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_A_dx (p) (f):
+ (âp)âð = â¼[f](pâð).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_S_dx (p) (f):
+ (âp)âð¦ = â¼[f](pâð¦).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_root (f) (p):
+ ââr. ð = âr & âpâr = â¼[f]p.
+#f #p @(list_ind_rcons ⦠p) -p
+[ /2 width=3 by ex2_intro/
+| #p * [ #n ] /2 width=3 by ex2_intro/
+]
+qed-.
+
+(* Advanced inversions with proj_path ***************************************)
+
+lemma unwind_path_inv_d_sn (k) (q) (p) (f):
+ (ð±kâq) = â¼[f]p â
+ ââr,h. ð = âr & (â¼[r]f)@â¨hâ© = k & ð = q & râð±h = p.
+#k #q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct -IH
+ /2 width=5 by ex4_2_intro/
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r #h #Hr #Hh #Hq #Hp destruct
+ /2 width=5 by ex4_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r #h #Hr #Hh #Hq #Hp destruct
+ /2 width=5 by ex4_2_intro/
+| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_m_sn (q) (p) (f):
+ (ðºâq) = â¼[f]p â â¥.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H /2 width=2 by/
+| <unwind_path_m_sn #H /2 width=2 by/
+| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_L_sn (q) (p) (f):
+ (ðâq) = â¼[f]p â
+ ââr1,r2. ð = âr1 & q = â¼[⫯â¼[r1]f]r2 & r1âðâr2 = p.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_L_sn #H destruct -IH
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_A_sn (q) (p) (f):
+ (ðâq) = â¼[f]p â
+ ââr1,r2. ð = âr1 & q = â¼[â¼[r1]f]r2 & r1âðâr2 = p.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct -IH
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_S_sn (q) (p) (f):
+ (ð¦âq) = â¼[f]p â
+ ââr1,r2. ð = âr1 & q = â¼[â¼[r1]f]r2 & r1âð¦âr2 = p.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct -IH
+ /2 width=5 by ex3_2_intro/
+]
+qed-.
+
+(* Inversions with proper condition for path ********************************)
+
+lemma unwind_inv_append_proper_dx (q2) (q1) (p) (f):
+ q2 ϵ ð â q1âq2 = â¼[f]p â
+ ââp1,p2. âp1 = q1 & â¼[â¼[p1]f]p2 = q2 & p1âp2 = p.
+#q2 #q1 elim q1 -q1
+[ #p #f #Hq2 <list_append_empty_sn #H destruct
+ /2 width=5 by ex3_2_intro/
+| * [ #n1 ] #q1 #IH #p #f #Hq2 <list_append_lcons_sn #H
+ [ elim (unwind_path_inv_d_sn ⦠H) -H #r1 #m1 #_ #_ #H0 #_ -IH
+ elim (eq_inv_list_empty_append ⦠H0) -H0 #_ #H0 destruct
+ elim Hq2 -Hq2 //
+ | elim (unwind_path_inv_m_sn ⦠H)
+ | elim (unwind_path_inv_L_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
+ elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
+ @(ex3_2_intro ⦠(r1âðâp1)) //
+ <structure_append <Hr1 -Hr1 //
+ | elim (unwind_path_inv_A_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
+ elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
+ @(ex3_2_intro ⦠(r1âðâp1)) //
+ <structure_append <Hr1 -Hr1 //
+ | elim (unwind_path_inv_S_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
+ elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
+ @(ex3_2_intro ⦠(r1âð¦âp1)) //
+ <structure_append <Hr1 -Hr1 //
+ ]
+]
+qed-.
+
+(* Inversions with inner condition for path *********************************)
+
+lemma unwind_inv_append_inner_sn (q1) (q2) (p) (f):
+ q1 ϵ ð â q1âq2 = â¼[f]p â
+ ââp1,p2. âp1 = q1 & â¼[â¼[p1]f]p2 = q2 & p1âp2 = p.
+#q1 @(list_ind_rcons ⦠q1) -q1
+[ #q2 #p #f #Hq1 <list_append_empty_sn #H destruct
+ /2 width=5 by ex3_2_intro/
+| #q1 * [ #n1 ] #_ #q2 #p #f #Hq2
+ [ elim (pic_inv_d_dx ⦠Hq2)
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_m_sn ⦠(sym_eq ⦠H2))
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_L_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
+ @(ex3_2_intro ⦠(p1âr2âð)) [1,3: // ]
+ [ <structure_append <structure_L_dx <Hr2 -Hr2 //
+ | <list_append_assoc <list_append_rcons_sn //
+ ]
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_A_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
+ @(ex3_2_intro ⦠(p1âr2âð)) [1,3: // ]
+ [ <structure_append <structure_A_dx <Hr2 -Hr2 //
+ | <list_append_assoc <list_append_rcons_sn //
+ ]
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_S_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
+ @(ex3_2_intro ⦠(p1âr2âð¦)) [1,3: // ]
+ [ <structure_append <structure_S_dx <Hr2 -Hr2 //
+ | <list_append_assoc <list_append_rcons_sn //
+ ]
+ ]
+]
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_structure_depth.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_structure_depth.etc
new file mode 100644
index 000000000..577a95bba
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind2/unwind_structure_depth.etc
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind2/unwind.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/arith/nat_pred_succ.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+(* Basic constructions with structure and depth *****************************)
+
+lemma unwind_rmap_structure (p) (f):
+ (⫯*[âpâ]f) = â¼[âp]f.
+#p elim p -p //
+* [ #n ] #p #IH #f //
+[ <unwind_rmap_A_sn //
+| <unwind_rmap_S_sn //
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind.etc
new file mode 100644
index 000000000..87790b370
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind.etc
@@ -0,0 +1,189 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/relocation/sbr_pap_push.ma".
+include "delayed_updating/syntax/path.ma".
+include "delayed_updating/notation/functions/black_downtriangle_4.ma".
+include "delayed_updating/notation/functions/black_downtriangle_2.ma".
+include "ground/relocation/tr_pn.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+definition unwind_continuation (A:Type[0]) â
+ tr_map â path â A.
+
+(* Note: f is a stack of update functions *)
+rec definition unwind_gen (A:Type[0]) (k:unwind_continuation A) (f:tr_map) (p) on p â
+match p with
+[ list_empty â k f (ð)
+| list_lcons l q â
+ match l with
+ [ label_d n â
+ match q with
+ [ list_empty â unwind_gen (A) (λg,p. k g (ð±(fâ@â¨nâ©)âp)) (fâ@â¨nâ©â«¯âf) q
+ | list_lcons _ _ â unwind_gen (A) k (fâ@â¨nâ©â«¯âf) q
+ ]
+ | label_m â unwind_gen (A) k f q
+ | label_L â unwind_gen (A) (λg,p. k g (ðâp)) (⫯f) q
+ | label_A â unwind_gen (A) (λg,p. k g (ðâp)) f q
+ | label_S â unwind_gen (A) (λg,p. k g (ð¦âp)) f q
+ ]
+].
+
+interpretation
+ "unwind (gneric)"
+ 'BlackDownTriangle A k f p = (unwind_gen A k f p).
+
+definition proj_path: unwind_continuation ⦠â
+ λf,p.p.
+
+definition proj_rmap: unwind_continuation ⦠â
+ λf,p.f.
+
+interpretation
+ "unwind (path)"
+ 'BlackDownTriangle f p = (unwind_gen ? proj_path f p).
+
+interpretation
+ "unwind (relocation map)"
+ 'BlackDownTriangle p f = (unwind_gen ? proj_rmap f p).
+
+(* Basic constructions ******************************************************)
+
+lemma unwind_empty (A) (k) (f):
+ k f (ð) = â¼{A}â¨k, f, ðâ©.
+// qed.
+
+lemma unwind_d_empty_sn (A) (k) (n) (f):
+ â¼â¨(λg,p. k g (ð±(fâ@â¨nâ©)âp)), fâ@â¨nâ©â«¯âf, ðâ© = â¼{A}â¨k, f, ð±nâðâ©.
+// qed.
+
+lemma unwind_d_lcons_sn (A) (k) (p) (l) (n) (f):
+ â¼â¨k, fâ@â¨nâ©â«¯âf, lâpâ© = â¼{A}â¨k, f, ð±nâlâpâ©.
+// qed.
+
+lemma unwind_m_sn (A) (k) (p) (f):
+ â¼â¨k, f, pâ© = â¼{A}â¨k, f, ðºâpâ©.
+// qed.
+
+lemma unwind_L_sn (A) (k) (p) (f):
+ â¼â¨(λg,p. k g (ðâp)), ⫯f, pâ© = â¼{A}â¨k, f, ðâpâ©.
+// qed.
+
+lemma unwind_A_sn (A) (k) (p) (f):
+ â¼â¨(λg,p. k g (ðâp)), f, pâ© = â¼{A}â¨k, f, ðâpâ©.
+// qed.
+
+lemma unwind_S_sn (A) (k) (p) (f):
+ â¼â¨(λg,p. k g (ð¦âp)), f, pâ© = â¼{A}â¨k, f, ð¦âpâ©.
+// qed.
+
+(* Basic constructions with proj_path ***************************************)
+
+lemma unwind_path_empty (f):
+ (ð) = â¼[f]ð.
+// qed.
+
+lemma unwind_path_d_empty_sn (f) (n):
+ ð±(fâ@â¨nâ©)âð = â¼[f](ð±nâð).
+// qed.
+
+lemma unwind_path_d_lcons_sn (f) (p) (l) (n):
+ â¼[fâ@â¨nâ©â«¯âf](lâp) = â¼[f](ð±nâlâp).
+// qed.
+
+lemma unwind_path_m_sn (f) (p):
+ â¼[f]p = â¼[f](ðºâp).
+// qed.
+
+(* Basic constructions with proj_rmap ***************************************)
+
+lemma unwind_rmap_empty (f):
+ f = â¼[ð]f.
+// qed.
+
+lemma unwind_rmap_d_sn (f) (p) (n):
+ â¼[p](fâ@â¨nâ©â«¯âf) = â¼[ð±nâp]f.
+#f * // qed.
+
+lemma unwind_rmap_m_sn (f) (p):
+ â¼[p]f = â¼[ðºâp]f.
+// qed.
+
+lemma unwind_rmap_L_sn (f) (p):
+ â¼[p](⫯f) = â¼[ðâp]f.
+// qed.
+
+lemma unwind_rmap_A_sn (f) (p):
+ â¼[p]f = â¼[ðâp]f.
+// qed.
+
+lemma unwind_rmap_S_sn (f) (p):
+ â¼[p]f = â¼[ð¦âp]f.
+// qed.
+
+(* Advanced constructions with proj_rmap and path_append ********************)
+
+lemma unwind_rmap_append (p2) (p1) (f):
+ â¼[p2]â¼[p1]f = â¼[p1âp2]f.
+#p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
+[ <unwind_rmap_m_sn <unwind_rmap_m_sn //
+| <unwind_rmap_A_sn <unwind_rmap_A_sn //
+| <unwind_rmap_S_sn <unwind_rmap_S_sn //
+]
+qed.
+
+(* Advanced constructions with proj_rmap and path_rcons *********************)
+
+lemma unwind_rmap_d_dx (f) (p) (n):
+ (â¼[p]f)â@â¨nâ©â«¯ââ¼[p]f = â¼[pâð±n]f.
+// qed.
+
+lemma unwind_rmap_m_dx (f) (p):
+ â¼[p]f = â¼[pâðº]f.
+// qed.
+
+lemma unwind_rmap_L_dx (f) (p):
+ (⫯â¼[p]f) = â¼[pâð]f.
+// qed.
+
+lemma unwind_rmap_A_dx (f) (p):
+ â¼[p]f = â¼[pâð]f.
+// qed.
+
+lemma unwind_rmap_S_dx (f) (p):
+â¼[p]f = â¼[pâð¦]f.
+// qed.
+
+lemma unwind_rmap_pap_d_dx (f) (p) (n) (m):
+ m+â¼[p]fâ@â¨nâ© = â¼[pâð±n]fâ@â¨mâ©.
+#f #p #n #m
+<unwind_rmap_d_dx <sbr_push_pap //
+qed.
+
+(* Advanced eliminations with path ******************************************)
+
+lemma path_ind_unwind (Q:predicate â¦):
+ Q (ð) â
+ (ân. Q (ð) â Q (ð±nâð)) â
+ (ân,l,p. Q (lâp) â Q (ð±nâlâp)) â
+ (âp. Q p â Q (ðºâp)) â
+ (âp. Q p â Q (ðâp)) â
+ (âp. Q p â Q (ðâp)) â
+ (âp. Q p â Q (ð¦âp)) â
+ âp. Q p.
+#Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #p
+elim p -p [| * [ #n * ] ]
+/2 width=1 by/
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_constructors.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_constructors.etc
new file mode 100644
index 000000000..4849ecf6d
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_constructors.etc
@@ -0,0 +1,44 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind_prototerm_eq.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+include "delayed_updating/relocation/sbr_push_uni.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+(* Constructions with constructors for prototerm ****************************)
+
+lemma unwind_iref_sn (f) (t:prototerm) (n:pnat):
+ â¼[fâ@â¨nâ©â«¯âf]t â â¼[f](ðn.t).
+#f #t #n #p * #q #Hq #H0 destruct
+@(ex2_intro ⦠(ð±nâðºâq))
+/2 width=1 by in_comp_iref/
+qed-.
+
+lemma unwind_iref_dx (f) (t) (n:pnat):
+ â¼[f](ðn.t) â â¼[fâ@â¨nâ©â«¯âf]t.
+#f #t #n #p * #q #Hq #H0 destruct
+elim (in_comp_inv_iref ⦠Hq) -Hq #p #Hp #Ht destruct
+/2 width=1 by in_comp_unwind_bi/
+qed-.
+
+lemma unwind_iref (f) (t) (n:pnat):
+ â¼[fâ@â¨nâ©â«¯âf]t â â¼[f](ðn.t).
+/3 width=1 by conj, unwind_iref_sn, unwind_iref_dx/
+qed.
+
+lemma unwind_iref_id (t) (n:pnat):
+ â¼[ð®â¨nâ©]t â â¼[ð¢](ðn.t).
+// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_depth.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_depth.etc
new file mode 100644
index 000000000..920036093
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_depth.etc
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/relocation/tr_uni_compose.ma".
+include "ground/lib/stream_tls_plus.ma".
+include "ground/lib/stream_eq_eq.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+(* Constructions with depth *************************************************)
+
+lemma tls_succ_unwind (q) (p) (f):
+ â¼[p]f â â*[ââqâ]â¼[pâðâq]f.
+#q @(list_ind_rcons ⦠q) -q //
+#q * [ #n ] #IH #p #f //
+<depth_d_dx >list_cons_shift <list_append_assoc <unwind_rmap_d_dx
+/3 width=3 by tr_tls_compose_uni_sn, stream_eq_trans/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_eq.etc
new file mode 100644
index 000000000..78d755b50
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_eq.etc
@@ -0,0 +1,124 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind.ma".
+include "delayed_updating/relocation/sbr_pap_id.ma".
+include "delayed_updating/relocation/sbr_pap_eq.ma".
+include "delayed_updating/relocation/sbr_push_eq.ma".
+include "ground/relocation/tr_pn_eq.ma".
+(*
+include "ground/lib/stream_tls.ma".
+*)
+
+(* UNWIND FOR PATH **********************************************************)
+
+definition unwind_exteq (A): relation2 (unwind_continuation A) (unwind_continuation A) â
+ λk1,k2. âf1,f2,p. f1 â f2 â k1 f1 p = k2 f2 p.
+
+interpretation
+ "extensional equivalence (unwind continuation)"
+ 'RingEq A k1 k2 = (unwind_exteq A k1 k2).
+
+(* Constructions with unwind_exteq ******************************************)
+
+lemma unwind_eq_repl (A) (p) (k1) (k2):
+ k1 â{A} k2 â stream_eq_repl ⦠(λf1,f2. â¼â¨k1, f1, pâ© = â¼â¨k2, f2, pâ©).
+#A #p @(path_ind_unwind ⦠p) -p [| #n #IH | #n #l0 #q #IH |*: #q #IH ]
+#k1 #k2 #Hk #f1 #f2 #Hf
+[ <unwind_empty <unwind_empty /2 width=1 by/
+| <unwind_d_empty_sn <unwind_d_empty_sn <(sbr_pap_eq_repl_sn ⦠Hf)
+ /3 width=1 by sbr_push_eq_repl_dx/
+| <unwind_d_lcons_sn <unwind_d_lcons_sn <(sbr_pap_eq_repl_sn ⦠Hf)
+ /3 width=1 by sbr_push_eq_repl_dx/
+| /2 width=1 by/
+| /3 width=1 by tr_push_eq_repl/
+| /3 width=1 by/
+| /3 width=1 by/
+]
+qed-.
+
+(* Advanced constructions ***************************************************)
+
+lemma unwind_lcons_alt (A) (k) (f) (p) (l): k â k â
+ â¼â¨Î»g,p2. k g (lâp2), f, pâ© = â¼{A}â¨Î»g,p2. k g ((lâð)âp2), f, pâ©.
+#A #k #f #p #l #Hk
+@unwind_eq_repl // #g1 #g2 #p2 #Hg @Hk -Hk // (**) (* auto fail *)
+qed.
+
+lemma unwind_append_rcons_sn (A) (k) (f) (p1) (p) (l): k â k â
+ â¼â¨Î»g,p2. k g (p1âlâp2), f, pâ© = â¼{A}â¨Î»g,p2. k g (p1âlâp2), f, pâ©.
+#A #k #f #p1 #p #l #Hk
+@unwind_eq_repl // #g1 #g2 #p2 #Hg
+<list_append_rcons_sn @Hk -Hk // (**) (* auto fail *)
+qed.
+
+(* Advanced constructions with proj_path ************************************)
+
+lemma proj_path_proper:
+ proj_path â proj_path.
+// qed.
+
+lemma unwind_path_eq_repl (p):
+ stream_eq_repl ⦠(λf1,f2. â¼[f1]p = â¼[f2]p).
+/2 width=1 by unwind_eq_repl/ qed.
+
+lemma unwind_path_append_sn (p) (f) (q):
+ qââ¼[f]p = â¼â¨(λg,p. proj_path g (qâp)), f, pâ©.
+#p @(path_ind_unwind ⦠p) -p // [ #n #l #p |*: #p ] #IH #f #q
+[ <unwind_d_lcons_sn <unwind_d_lcons_sn <IH -IH //
+| <unwind_m_sn <unwind_m_sn //
+| <unwind_L_sn <unwind_L_sn >unwind_lcons_alt // >unwind_append_rcons_sn //
+ <IH <IH -IH <list_append_rcons_sn //
+| <unwind_A_sn <unwind_A_sn >unwind_lcons_alt >unwind_append_rcons_sn //
+ <IH <IH -IH <list_append_rcons_sn //
+| <unwind_S_sn <unwind_S_sn >unwind_lcons_alt >unwind_append_rcons_sn //
+ <IH <IH -IH <list_append_rcons_sn //
+]
+qed.
+
+lemma unwind_path_lcons (f) (p) (l):
+ lââ¼[f]p = â¼â¨(λg,p. proj_path g (lâp)), f, pâ©.
+#f #p #l
+>unwind_lcons_alt <unwind_path_append_sn //
+qed.
+
+lemma unwind_path_L_sn (f) (p):
+ (ðââ¼[⫯f]p) = â¼[f](ðâp).
+// qed.
+
+lemma unwind_path_A_sn (f) (p):
+ (ðââ¼[f]p) = â¼[f](ðâp).
+// qed.
+
+lemma unwind_path_S_sn (f) (p):
+ (ð¦ââ¼[f]p) = â¼[f](ð¦âp).
+// qed.
+
+lemma unwind_path_after_id_sn (p) (f):
+ â¼[ð¢]â¼[f]p = â¼[f]p.
+#p @(path_ind_unwind ⦠p) -p // #p #IH #f
+[ <unwind_path_d_empty_sn <unwind_path_d_empty_sn //
+| <unwind_path_L_sn <unwind_path_L_sn //
+]
+qed.
+
+(* Advanced constructions with proj_rmap and stream_tls *********************)
+(* COMMENT
+lemma unwind_rmap_tls_d_dx (f) (p) (m:pnat) (n):
+ â*[m]â¼[p]f â â*[m]â¼[pâð±n]f.
+#f #p #m #n
+<unwind_rmap_d_dx
+/2 width=1 by tr_tls_compose_uni_sn/
+qed.
+*)
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_fsubst.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_fsubst.etc
new file mode 100644
index 000000000..411c5621a
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_fsubst.etc
@@ -0,0 +1,61 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind_prototerm_eq.ma".
+include "delayed_updating/unwind3/unwind_structure.ma".
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/syntax/preterm.ma".
+include "delayed_updating/syntax/prototerm_proper.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+(* Constructions with fsubst ************************************************)
+
+lemma unwind_fsubst_sn (f) (t) (u) (p): u ϵ ð â
+ (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u] â â¼[f](t[âpâu]).
+#f #t #u #p #Hu #ql * *
+[ #rl * #r #Hr #H1 #H2 destruct
+ >unwind_append_proper_dx
+ /4 width=5 by in_comp_unwind_bi, in_ppc_comp_trans, or_introl, ex2_intro/
+| * #q #Hq #H1 #H0
+ @(ex2_intro ⦠H1) @or_intror @conj // *
+ [ <list_append_empty_dx #H2 destruct
+ elim (unwind_path_root f q) #r #_ #Hr /2 width=2 by/
+ | #l #r #H2 destruct
+ @H0 -H0 [| <unwind_append_proper_dx /2 width=3 by ppc_lcons/ ]
+ ]
+]
+qed-.
+
+lemma unwind_fsubst_dx (f) (t) (u) (p): u ϵ ð â p ϵ âµt â t ϵ ð â
+ â¼[f](t[âpâu]) â (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u].
+#f #t #u #p #Hu #H1p #H2p #ql * #q * *
+[ #r #Hu #H1 #H2 destruct
+ @or_introl @ex2_intro
+ [|| <unwind_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
+ /2 width=3 by ex2_intro/
+| #Hq #H0 #H1 destruct
+ @or_intror @conj [ /2 width=1 by in_comp_unwind_bi/ ] *
+ [ <list_append_empty_dx #Hr @(H0 ⦠(ð)) -H0
+ <list_append_empty_dx @H2p -H2p /2 width=1 by prototerm_in_comp_root/
+ | #l #r #Hr
+ elim (unwind_inv_append_proper_dx ⦠Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
+ lapply (H2p ⦠Hs1) -H2p -Hs1 /2 width=2 by ex_intro/
+ ]
+]
+qed-.
+
+lemma unwind_fsubst (f) (t) (u) (p): u ϵ ð â p ϵ âµt â t ϵ ð â
+ (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u] â â¼[f](t[âpâu]).
+/4 width=3 by unwind_fsubst_sn, conj, unwind_fsubst_dx/ qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_length.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_length.etc
new file mode 100644
index 000000000..7514a68cf
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_length.etc
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/lib/stream_tls_plus.ma".
+include "ground/lib/stream_eq.ma".
+(*
+include "ground/relocation/tr_uni_compose.ma".
+include "ground/lib/stream_eq_eq.ma".
+*)
+(* UNWIND FOR PATH **********************************************************)
+
+(* Constructions with list_length ********************************************)
+
+axiom tls_unwind (p) (f):
+ f â â*[âpâ]â¼[p]f.
+(* COMMENT
+#q @(list_ind_rcons ⦠q) -q //
+#q * [ #n ] #IH #f //
+<depth_d_dx >list_cons_shift <list_append_assoc <unwind_rmap_d_dx
+/3 width=3 by tr_tls_compose_uni_sn, stream_eq_trans/
+qed.
+*)
\ No newline at end of file
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_lift.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_lift.etc
new file mode 100644
index 000000000..9530004ca
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_lift.etc
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind_structure.ma".
+include "delayed_updating/substitution/lift_structure.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+(* Constructions with lift **************************************************)
+
+lemma pippo (p) (n:pnat) (f):
+ â[ð®â¨nâ©]â¼[â*[n]f]p = â¼[ð®â¨nâ©âf]p.
+#p @(list_ind_rcons ⦠p) -p //
+#p * [ #m ] #IH #n #f //
+[
+| <unwind_path_m_dx
+
+ //
+<depth_d_dx >list_cons_shift <list_append_assoc <unwind_rmap_d_dx
+/3 width=3 by tr_tls_compose_uni_sn, stream_eq_trans/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_preterm_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_preterm_eq.etc
new file mode 100644
index 000000000..d245cb1bf
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_preterm_eq.etc
@@ -0,0 +1,68 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground/lib/subset_equivalence.ma".
+include "delayed_updating/syntax/path_structure_inner.ma".
+include "delayed_updating/syntax/preterm.ma".
+include "delayed_updating/unwind3/unwind_structure.ma".
+include "delayed_updating/unwind3/unwind_prototerm.ma".
+
+(* UNWIND FOR PRETERM *******************************************************)
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma unwind_grafted_sn (f) (t) (p): p ϵ ð â
+ â¼[â¼[p]f](tâp) â (â¼[f]t)â(âp).
+#f #t #p #Hp #q * #r #Hr #H0 destruct
+@(ex2_intro ⦠Hr) -Hr
+<unwind_append_inner_sn //
+qed-.
+
+lemma unwind_grafted_dx (f) (t) (p): p ϵ ð â p ϵ âµt â t ϵ ð â
+ (â¼[f]t)â(âp) â â¼[â¼[p]f](tâp).
+#f #t #p #H1p #H2p #Ht #q * #r #Hr #H0
+elim (unwind_inv_append_inner_sn ⦠(sym_eq ⦠H0)) -H0 //
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+<(Ht ⦠Hp0) [|*: /2 width=2 by ex_intro/ ] -p
+/2 width=1 by in_comp_unwind_bi/
+qed-.
+
+lemma unwind_grafted (f) (t) (p): p ϵ ð â p ϵ âµt â t ϵ ð â
+ â¼[â¼[p]f](tâp) â (â¼[f]t)â(âp).
+/3 width=1 by unwind_grafted_sn, conj, unwind_grafted_dx/ qed.
+
+
+lemma unwind_grafted_S_dx (f) (t) (p): p ϵ âµt â t ϵ ð â
+ (â¼[f]t)â((âp)âð¦) â â¼[â¼[p]f](tâ(pâð¦)).
+#f #t #p #Hp #Ht #q * #r #Hr
+<list_append_rcons_sn #H0
+elim (unwind_inv_append_proper_dx ⦠(sym_eq ⦠H0)) -H0 //
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+<(Ht ⦠Hp0) [|*: /2 width=2 by ex_intro/ ] -p
+elim (unwind_path_inv_S_sn ⦠(sym_eq ⦠Hq0)) -Hq0
+#r1 #r2 #Hr1 #Hr2 #H0 destruct
+lapply (preterm_in_root_append_inv_structure_empty_dx ⦠p0 ⦠Ht Hr1)
+[ /2 width=2 by ex_intro/ ] -Hr1 #Hr1 destruct
+/2 width=1 by in_comp_unwind_bi/
+qed-.
+
+lemma unwind_grafted_S (f) (t) (p): p ϵ âµt â t ϵ ð â
+ â¼[â¼[p]f](tâ(pâð¦)) â (â¼[f]t)â((âp)âð¦).
+#f #t #p #Hp #Ht
+@conj
+[ >unwind_rmap_S_dx >structure_S_dx
+ @unwind_grafted_sn //
+| /2 width=1 by unwind_grafted_S_dx/
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_prototerm.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_prototerm.etc
new file mode 100644
index 000000000..c4a103b61
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_prototerm.etc
@@ -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/unwind3/unwind.ma".
+include "delayed_updating/syntax/prototerm.ma".
+include "ground/lib/subset_ext.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+interpretation
+ "unwind (prototerm)"
+ 'BlackDownTriangle f t = (subset_ext_f1 ? ? (unwind_gen ? proj_path f) t).
+
+(* Basic constructions ******************************************************)
+
+lemma in_comp_unwind_bi (f) (p) (t):
+ p ϵ t â â¼[f]p ϵ â¼[f]t.
+/2 width=1 by subset_in_ext_f1_dx/
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_prototerm_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_prototerm_eq.etc
new file mode 100644
index 000000000..01d302f3e
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_prototerm_eq.etc
@@ -0,0 +1,41 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground/lib/subset_ext_equivalence.ma".
+include "delayed_updating/unwind3/unwind_eq.ma".
+include "delayed_updating/unwind3/unwind_prototerm.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma unwind_term_eq_repl_sn (f1) (f2) (t):
+ f1 â f2 â â¼[f1]t â â¼[f2]t.
+/3 width=1 by subset_equivalence_ext_f1_exteq, unwind_path_eq_repl/
+qed.
+
+lemma unwind_term_eq_repl_dx (f) (t1) (t2):
+ t1 â t2 â â¼[f]t1 â â¼[f]t2.
+/2 width=1 by subset_equivalence_ext_f1_bi/
+qed.
+
+lemma unwind_term_after_id_sn (f) (t):
+ â¼[ð¢]â¼[f]t â â¼[f]t.
+#f #t @subset_eq_trans
+[
+| @subset_inclusion_ext_f1_compose
+| @subset_equivalence_ext_f1_exteq
+ #p @unwind_path_after_id_sn
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_structure.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_structure.etc
new file mode 100644
index 000000000..c52a43871
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_structure.etc
@@ -0,0 +1,269 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind_eq.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_inner.ma".
+include "delayed_updating/syntax/path_proper.ma".
+include "ground/xoa/ex_4_2.ma".
+
+(* UNWIND FOR PATH *********************************************************)
+
+(* Basic constructions with structure **************************************)
+
+lemma structure_unwind (p) (f):
+ âp = ââ¼[f]p.
+#p @(path_ind_unwind ⦠p) -p // #p #IH #f
+<unwind_path_L_sn //
+qed.
+
+lemma unwind_structure (p) (f):
+ âp = â¼[f]âp.
+#p @(path_ind_unwind ⦠p) -p //
+qed.
+
+(* Destructions with structure **********************************************)
+
+lemma unwind_des_structure (q) (p) (f):
+ âq = â¼[f]p â âq = âp.
+// qed-.
+
+(* Constructions with proper condition for path *****************************)
+
+lemma unwind_append_proper_dx (p2) (p1) (f): p2 ϵ ð â
+ (âp1)â(â¼[â¼[p1]f]p2) = â¼[f](p1âp2).
+#p2 #p1 @(path_ind_unwind ⦠p1) -p1 //
+[ #n | #n #l #p1 |*: #p1 ] #IH #f #Hp2
+[ elim (ppc_inv_lcons ⦠Hp2) -Hp2 #l #q #H destruct //
+| <unwind_path_d_lcons_sn <IH //
+| <unwind_path_m_sn <IH //
+| <unwind_path_L_sn <IH //
+| <unwind_path_A_sn <IH //
+| <unwind_path_S_sn <IH //
+]
+qed-.
+
+(* Constructions with inner condition for path ******************************)
+
+lemma unwind_append_inner_sn (p1) (p2) (f): p1 ϵ ð â
+ (âp1)â(â¼[â¼[p1]f]p2) = â¼[f](p1âp2).
+#p1 @(list_ind_rcons ⦠p1) -p1 // #p1 *
+[ #n ] #_ #p2 #f #Hp1
+[ elim (pic_inv_d_dx ⦠Hp1)
+| <list_append_rcons_sn <unwind_append_proper_dx //
+| <list_append_rcons_sn <unwind_append_proper_dx //
+ <structure_L_dx <list_append_rcons_sn //
+| <list_append_rcons_sn <unwind_append_proper_dx //
+ <structure_A_dx <list_append_rcons_sn //
+| <list_append_rcons_sn <unwind_append_proper_dx //
+ <structure_S_dx <list_append_rcons_sn //
+]
+qed-.
+
+(* Advanced constructions with proj_path ************************************)
+
+lemma unwind_path_d_empty_dx (n) (p) (f):
+ (âp)âð±((â¼[p]f)â@â¨nâ©) = â¼[f](pâð±n).
+#n #p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_m_dx (p) (f):
+ âp = â¼[f](pâðº).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_L_dx (p) (f):
+ (âp)âð = â¼[f](pâð).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_A_dx (p) (f):
+ (âp)âð = â¼[f](pâð).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_S_dx (p) (f):
+ (âp)âð¦ = â¼[f](pâð¦).
+#p #f <unwind_append_proper_dx //
+qed.
+
+lemma unwind_path_root (f) (p):
+ ââr. ð = âr & âpâr = â¼[f]p.
+#f #p @(list_ind_rcons ⦠p) -p
+[ /2 width=3 by ex2_intro/
+| #p * [ #n ] /2 width=3 by ex2_intro/
+]
+qed-.
+
+(* Advanced inversions with proj_path ***************************************)
+
+lemma unwind_path_inv_d_sn (k) (q) (p) (f):
+ (ð±kâq) = â¼[f]p â
+ ââr,h. ð = âr & (â¼[r]f)â@â¨hâ© = k & ð = q & râð±h = p.
+#k #q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct -IH
+ /2 width=5 by ex4_2_intro/
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r #h #Hr #Hh #Hq #Hp destruct
+ /2 width=5 by ex4_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r #h #Hr #Hh #Hq #Hp destruct
+ /2 width=5 by ex4_2_intro/
+| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_m_sn (q) (p) (f):
+ (ðºâq) = â¼[f]p â â¥.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H /2 width=2 by/
+| <unwind_path_m_sn #H /2 width=2 by/
+| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_L_sn (q) (p) (f):
+ (ðâq) = â¼[f]p â
+ ââr1,r2. ð = âr1 & q = â¼[⫯â¼[r1]f]r2 & r1âðâr2 = p.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_L_sn #H destruct -IH
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_A_sn (q) (p) (f):
+ (ðâq) = â¼[f]p â
+ ââr1,r2. ð = âr1 & q = â¼[â¼[r1]f]r2 & r1âðâr2 = p.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct -IH
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_S_sn #H destruct
+]
+qed-.
+
+lemma unwind_path_inv_S_sn (q) (p) (f):
+ (ð¦âq) = â¼[f]p â
+ ââr1,r2. ð = âr1 & q = â¼[â¼[r1]f]r2 & r1âð¦âr2 = p.
+#q #p @(path_ind_unwind ⦠p) -p
+[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
+[ <unwind_path_empty #H destruct
+| <unwind_path_d_empty_sn #H destruct
+| <unwind_path_d_lcons_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/
+| <unwind_path_m_sn #H
+ elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
+ /2 width=5 by ex3_2_intro/| <unwind_path_L_sn #H destruct
+| <unwind_path_A_sn #H destruct
+| <unwind_path_S_sn #H destruct -IH
+ /2 width=5 by ex3_2_intro/
+]
+qed-.
+
+(* Inversions with proper condition for path ********************************)
+
+lemma unwind_inv_append_proper_dx (q2) (q1) (p) (f):
+ q2 ϵ ð â q1âq2 = â¼[f]p â
+ ââp1,p2. âp1 = q1 & â¼[â¼[p1]f]p2 = q2 & p1âp2 = p.
+#q2 #q1 elim q1 -q1
+[ #p #f #Hq2 <list_append_empty_sn #H destruct
+ /2 width=5 by ex3_2_intro/
+| * [ #n1 ] #q1 #IH #p #f #Hq2 <list_append_lcons_sn #H
+ [ elim (unwind_path_inv_d_sn ⦠H) -H #r1 #m1 #_ #_ #H0 #_ -IH
+ elim (eq_inv_list_empty_append ⦠H0) -H0 #_ #H0 destruct
+ elim Hq2 -Hq2 //
+ | elim (unwind_path_inv_m_sn ⦠H)
+ | elim (unwind_path_inv_L_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
+ elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
+ @(ex3_2_intro ⦠(r1âðâp1)) //
+ <structure_append <Hr1 -Hr1 //
+ | elim (unwind_path_inv_A_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
+ elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
+ @(ex3_2_intro ⦠(r1âðâp1)) //
+ <structure_append <Hr1 -Hr1 //
+ | elim (unwind_path_inv_S_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
+ elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
+ @(ex3_2_intro ⦠(r1âð¦âp1)) //
+ <structure_append <Hr1 -Hr1 //
+ ]
+]
+qed-.
+
+(* Inversions with inner condition for path *********************************)
+
+lemma unwind_inv_append_inner_sn (q1) (q2) (p) (f):
+ q1 ϵ ð â q1âq2 = â¼[f]p â
+ ââp1,p2. âp1 = q1 & â¼[â¼[p1]f]p2 = q2 & p1âp2 = p.
+#q1 @(list_ind_rcons ⦠q1) -q1
+[ #q2 #p #f #Hq1 <list_append_empty_sn #H destruct
+ /2 width=5 by ex3_2_intro/
+| #q1 * [ #n1 ] #_ #q2 #p #f #Hq2
+ [ elim (pic_inv_d_dx ⦠Hq2)
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_m_sn ⦠(sym_eq ⦠H2))
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_L_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
+ @(ex3_2_intro ⦠(p1âr2âð)) [1,3: // ]
+ [ <structure_append <structure_L_dx <Hr2 -Hr2 //
+ | <list_append_assoc <list_append_rcons_sn //
+ ]
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_A_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
+ @(ex3_2_intro ⦠(p1âr2âð)) [1,3: // ]
+ [ <structure_append <structure_A_dx <Hr2 -Hr2 //
+ | <list_append_assoc <list_append_rcons_sn //
+ ]
+ | <list_append_rcons_sn #H0
+ elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
+ elim (unwind_path_inv_S_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
+ @(ex3_2_intro ⦠(p1âr2âð¦)) [1,3: // ]
+ [ <structure_append <structure_S_dx <Hr2 -Hr2 //
+ | <list_append_assoc <list_append_rcons_sn //
+ ]
+ ]
+]
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_structure_depth.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_structure_depth.etc
new file mode 100644
index 000000000..fdb7d781b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/unwind3/unwind_structure_depth.etc
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/unwind3/unwind.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "ground/arith/nat_pred_succ.ma".
+
+(* UNWIND FOR PATH *********************************************************)
+
+(* Basic constructions with structure and depth ****************************)
+
+lemma unwind_rmap_structure (p) (f):
+ (⫯*[âpâ]f) = â¼[âp]f.
+#p elim p -p //
+* [ #n ] #p #IH #f //
+[ <unwind_rmap_A_sn //
+| <unwind_rmap_S_sn //
+]
+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
deleted file mode 100644
index 1d8b45295..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_id.ma
+++ /dev/null
@@ -1,30 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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 = â[ð¢]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
deleted file mode 100644
index cc7569284..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
+++ /dev/null
@@ -1,33 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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 â â[ð¢]t.
-#t #p #Hp
->(lift_path_id p)
-/2 width=1 by in_comp_lift_bi/
-qed-.
-
-lemma lift_term_id_dx (t):
- â[ð¢]t â t.
-#t #p * #q #Hq #H destruct //
-qed-.
-
-lemma lift_term_id (t):
- t â â[ð¢]t.
-/3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind.ma
deleted file mode 100644
index 1713625e8..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind.ma
+++ /dev/null
@@ -1,189 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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 "ground/relocation/tr_compose_pap.ma".
-include "ground/relocation/tr_uni_pap.ma".
-include "delayed_updating/syntax/path.ma".
-include "delayed_updating/notation/functions/black_downtriangle_4.ma".
-include "delayed_updating/notation/functions/black_downtriangle_2.ma".
-
-(* UNWIND FOR PATH **********************************************************)
-
-definition unwind_continuation (A:Type[0]) â
-tr_map â path â A.
-
-rec definition unwind_gen (A:Type[0]) (k:unwind_continuation A) (f) (p) on p â
-match p with
-[ list_empty â k f (ð)
-| list_lcons l q â
- match l with
- [ label_d n â
- match q with
- [ list_empty â unwind_gen (A) (λg,p. k g (ð±(f@â¨nâ©)âp)) (fâð®â¨nâ©) q
- | list_lcons _ _ â unwind_gen (A) k (fâð®â¨nâ©) q
- ]
- | label_m â unwind_gen (A) k f q
- | label_L â unwind_gen (A) (λg,p. k g (ðâp)) (⫯f) q
- | label_A â unwind_gen (A) (λg,p. k g (ðâp)) f q
- | label_S â unwind_gen (A) (λg,p. k g (ð¦âp)) f q
- ]
-].
-
-interpretation
- "unwind (gneric)"
- 'BlackDownTriangle A k f p = (unwind_gen A k f p).
-
-definition proj_path: unwind_continuation ⦠â
- λf,p.p.
-
-definition proj_rmap: unwind_continuation ⦠â
- λf,p.f.
-
-interpretation
- "unwind (path)"
- 'BlackDownTriangle f p = (unwind_gen ? proj_path f p).
-
-interpretation
- "unwind (relocation map)"
- 'BlackDownTriangle p f = (unwind_gen ? proj_rmap f p).
-
-(* Basic constructions ******************************************************)
-
-lemma unwind_empty (A) (k) (f):
- k f (ð) = â¼{A}â¨k, f, ðâ©.
-// qed.
-
-lemma unwind_d_empty_sn (A) (k) (n) (f):
- â¼â¨(λg,p. k g (ð±(f@â¨nâ©)âp)), fâð®â¨ninj nâ©, ðâ© = â¼{A}â¨k, f,
-ð±nâðâ©.
-// qed.
-
-lemma unwind_d_lcons_sn (A) (k) (p) (l) (n) (f):
- â¼â¨k, fâð®â¨ninj nâ©, lâpâ© = â¼{A}â¨k, f, ð±nâlâpâ©.
-// qed.
-
-lemma unwind_m_sn (A) (k) (p) (f):
- â¼â¨k, f, pâ© = â¼{A}â¨k, f, ðºâpâ©.
-// qed.
-
-lemma unwind_L_sn (A) (k) (p) (f):
- â¼â¨(λg,p. k g (ðâp)), ⫯f, pâ© = â¼{A}â¨k, f, ðâpâ©.
-// qed.
-
-lemma unwind_A_sn (A) (k) (p) (f):
- â¼â¨(λg,p. k g (ðâp)), f, pâ© = â¼{A}â¨k, f, ðâpâ©.
-// qed.
-
-lemma unwind_S_sn (A) (k) (p) (f):
- â¼â¨(λg,p. k g (ð¦âp)), f, pâ© = â¼{A}â¨k, f, ð¦âpâ©.
-// qed.
-
-(* Basic constructions with proj_path ***************************************)
-
-lemma unwind_path_empty (f):
- (ð) = â¼[f]ð.
-// qed.
-
-lemma unwind_path_d_empty_sn (f) (n):
- ð±(f@â¨nâ©)âð = â¼[f](ð±nâð).
-// qed.
-
-lemma unwind_path_d_lcons_sn (f) (p) (l) (n):
- â¼[fâð®â¨ninj nâ©](lâp) = â¼[f](ð±nâlâp).
-// qed.
-
-lemma unwind_path_m_sn (f) (p):
- â¼[f]p = â¼[f](ðºâp).
-// qed.
-
-(* Basic constructions with proj_rmap ***************************************)
-
-lemma unwind_rmap_empty (f):
- f = â¼[ð]f.
-// qed.
-
-lemma unwind_rmap_d_sn (f) (p) (n):
- â¼[p](fâð®â¨ninj nâ©) = â¼[ð±nâp]f.
-#f * // qed.
-
-lemma unwind_rmap_m_sn (f) (p):
- â¼[p]f = â¼[ðºâp]f.
-// qed.
-
-lemma unwind_rmap_L_sn (f) (p):
- â¼[p](⫯f) = â¼[ðâp]f.
-// qed.
-
-lemma unwind_rmap_A_sn (f) (p):
- â¼[p]f = â¼[ðâp]f.
-// qed.
-
-lemma unwind_rmap_S_sn (f) (p):
- â¼[p]f = â¼[ð¦âp]f.
-// qed.
-
-(* Advanced constructions with proj_rmap and path_append ********************)
-
-lemma unwind_rmap_append (p2) (p1) (f):
- â¼[p2]â¼[p1]f = â¼[p1âp2]f.
-#p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
-[ <unwind_rmap_m_sn <unwind_rmap_m_sn //
-| <unwind_rmap_A_sn <unwind_rmap_A_sn //
-| <unwind_rmap_S_sn <unwind_rmap_S_sn //
-]
-qed.
-
-(* Advanced constructions with proj_rmap and path_rcons *********************)
-
-lemma unwind_rmap_d_dx (f) (p) (n):
- (â¼[p]f)âð®â¨ninj nâ© = â¼[pâð±n]f.
-// qed.
-
-lemma unwind_rmap_m_dx (f) (p):
- â¼[p]f = â¼[pâðº]f.
-// qed.
-
-lemma unwind_rmap_L_dx (f) (p):
- (⫯â¼[p]f) = â¼[pâð]f.
-// qed.
-
-lemma unwind_rmap_A_dx (f) (p):
- â¼[p]f = â¼[pâð]f.
-// qed.
-
-lemma unwind_rmap_S_dx (f) (p):
-â¼[p]f = â¼[pâð¦]f.
-// qed.
-
-lemma unwind_rmap_pap_d_dx (f) (p) (n) (m):
- â¼[p]f@â¨m+nâ© = â¼[pâð±n]f@â¨mâ©.
-#f #p #n #m
-<unwind_rmap_d_dx <tr_compose_pap <tr_uni_pap //
-qed.
-
-(* Advanced eliminations with path ******************************************)
-
-lemma path_ind_unwind (Q:predicate â¦):
- Q (ð) â
- (ân. Q (ð) â Q (ð±nâð)) â
- (ân,l,p. Q (lâp) â Q (ð±nâlâp)) â
- (âp. Q p â Q (ðºâp)) â
- (âp. Q p â Q (ðâp)) â
- (âp. Q p â Q (ðâp)) â
- (âp. Q p â Q (ð¦âp)) â
- âp. Q p.
-#Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #p
-elim p -p [| * [ #n * ] ]
-/2 width=1 by/
-qed-.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_constructors.ma
deleted file mode 100644
index 93ddb2ef6..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_constructors.ma
+++ /dev/null
@@ -1,42 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind_prototerm_eq.ma".
-include "delayed_updating/syntax/prototerm_constructors.ma".
-
-(* UNWIND FOR PROTOTERM *****************************************************)
-
-lemma unwind_iref_after_sn (f) (t:prototerm) (n:pnat):
- â¼[fâð®â¨nâ©]t â â¼[f](ðn.t).
-#f #t #n #p * #q #Hq #H0 destruct
-@(ex2_intro ⦠(ð±nâðºâq))
-/2 width=1 by in_comp_iref/
-qed-.
-
-lemma unwind_iref_after_dx (f) (t) (n:pnat):
- â¼[f](ðn.t) â â¼[fâð®â¨nâ©]t.
-#f #t #n #p * #q #Hq #H0 destruct
-elim (in_comp_inv_iref ⦠Hq) -Hq #p #Hp #Ht destruct
-/2 width=1 by in_comp_unwind_bi/
-qed-.
-
-lemma unwind_iref_after (f) (t) (n:pnat):
- â¼[fâð®â¨nâ©]t â â¼[f](ðn.t).
-/3 width=1 by conj, unwind_iref_after_sn, unwind_iref_after_dx/
-qed.
-
-lemma unwind_iref (f) (t) (n:pnat):
- â¼[f]â¼[ð®â¨nâ©]t â â¼[f](ðn.t).
-/3 width=3 by unwind_term_after, subset_eq_trans/
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_depth.ma
deleted file mode 100644
index 8715fb514..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_depth.ma
+++ /dev/null
@@ -1,48 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind.ma".
-include "delayed_updating/syntax/path_depth.ma".
-include "ground/relocation/tr_id_compose.ma".
-include "ground/relocation/tr_compose_compose.ma".
-include "ground/relocation/tr_compose_pn.ma".
-include "ground/relocation/tr_compose_eq.ma".
-include "ground/relocation/tr_pn_eq.ma".
-include "ground/lib/stream_eq_eq.ma".
-
-(* UNWIND FOR PATH **********************************************************)
-
-(* Constructions with depth *************************************************)
-
-lemma unwind_rmap_decompose (p) (f):
- â¼[p]f â (⫯*[âpâ]f)â(â¼[p]ð¢).
-#p @(list_ind_rcons ⦠p) -p
-[ #f <unwind_rmap_empty <unwind_rmap_empty <tr_pushs_zero //
-| #p * [ #n ] #IH #f //
- [ <unwind_rmap_d_dx <unwind_rmap_d_dx <depth_d_dx
- @(stream_eq_trans ⦠(tr_compose_assoc â¦))
- /2 width=1 by tr_compose_eq_repl/
- | <unwind_rmap_L_dx <unwind_rmap_L_dx <depth_L_dx
- <tr_pushs_succ <tr_compose_push_bi
- /2 width=1 by tr_push_eq_repl/
- ]
-]
-qed.
-
-lemma unwind_rmap_pap_le (f) (p) (n):
- (â¼[p]ð¢)@â¨nâ© < ââpâ â (â¼[p]ð¢)@â¨nâ© = (â¼[p]f)@â¨nâ©.
-#f #p #n #Hn
->(tr_pap_eq_repl ⦠(â¼[p]f) ⦠(unwind_rmap_decompose â¦))
-<tr_compose_pap @tr_pap_pushs_le //
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_eq.ma
deleted file mode 100644
index b3c0b40e3..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_eq.ma
+++ /dev/null
@@ -1,122 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind.ma".
-include "ground/relocation/tr_uni_compose.ma".
-include "ground/relocation/tr_compose_compose.ma".
-include "ground/relocation/tr_compose_eq.ma".
-include "ground/relocation/tr_pn_eq.ma".
-
-(* UNWIND FOR PATH **********************************************************)
-
-definition unwind_exteq (A): relation2 (unwind_continuation A) (unwind_continuation A) â
- λk1,k2. âf1,f2,p. f1 â f2 â k1 f1 p = k2 f2 p.
-
-interpretation
- "extensional equivalence (unwind continuation)"
- 'RingEq A k1 k2 = (unwind_exteq A k1 k2).
-
-(* Constructions with unwind_exteq ******************************************)
-
-lemma unwind_eq_repl (A) (p) (k1) (k2):
- k1 â{A} k2 â stream_eq_repl ⦠(λf1,f2. â¼â¨k1, f1, pâ© = â¼â¨k2, f2, pâ©).
-#A #p @(path_ind_unwind ⦠p) -p [| #n #IH | #n #l0 #q #IH |*: #q #IH ]
-#k1 #k2 #Hk #f1 #f2 #Hf
-[ <unwind_empty <unwind_empty /2 width=1 by/
-| <unwind_d_empty_sn <unwind_d_empty_sn <(tr_pap_eq_repl ⦠Hf)
- /3 width=1 by tr_compose_eq_repl, stream_eq_refl/
-| <unwind_d_lcons_sn <unwind_d_lcons_sn
- /3 width=1 by tr_compose_eq_repl, stream_eq_refl/
-| /2 width=1 by/
-| /3 width=1 by tr_push_eq_repl/
-| /3 width=1 by/
-| /3 width=1 by/
-]
-qed-.
-
-(* Advanced constructions ***************************************************)
-
-lemma unwind_lcons_alt (A) (k) (f) (p) (l): k â k â
- â¼â¨Î»g,p2. k g (lâp2), f, pâ© = â¼{A}â¨Î»g,p2. k g ((lâð)âp2), f, pâ©.
-#A #k #f #p #l #Hk
-@unwind_eq_repl // #g1 #g2 #p2 #Hg @Hk -Hk // (**) (* auto fail *)
-qed.
-
-lemma unwind_append_rcons_sn (A) (k) (f) (p1) (p) (l): k â k â
- â¼â¨Î»g,p2. k g (p1âlâp2), f, pâ© = â¼{A}â¨Î»g,p2. k g (p1âlâp2), f, pâ©.
-#A #k #f #p1 #p #l #Hk
-@unwind_eq_repl // #g1 #g2 #p2 #Hg
-<list_append_rcons_sn @Hk -Hk // (**) (* auto fail *)
-qed.
-
-(* Advanced constructions with proj_path ************************************)
-
-lemma proj_path_proper:
- proj_path â proj_path.
-// qed.
-
-lemma unwind_path_eq_repl (p):
- stream_eq_repl ⦠(λf1,f2. â¼[f1]p = â¼[f2]p).
-/2 width=1 by unwind_eq_repl/ qed.
-
-lemma unwind_path_append_sn (p) (f) (q):
- qââ¼[f]p = â¼â¨(λg,p. proj_path g (qâp)), f, pâ©.
-#p @(path_ind_unwind ⦠p) -p // [ #n #l #p |*: #p ] #IH #f #q
-[ <unwind_d_lcons_sn <unwind_d_lcons_sn <IH -IH //
-| <unwind_m_sn <unwind_m_sn //
-| <unwind_L_sn <unwind_L_sn >unwind_lcons_alt // >unwind_append_rcons_sn //
- <IH <IH -IH <list_append_rcons_sn //
-| <unwind_A_sn <unwind_A_sn >unwind_lcons_alt >unwind_append_rcons_sn //
- <IH <IH -IH <list_append_rcons_sn //
-| <unwind_S_sn <unwind_S_sn >unwind_lcons_alt >unwind_append_rcons_sn //
- <IH <IH -IH <list_append_rcons_sn //
-]
-qed.
-
-lemma unwind_path_lcons (f) (p) (l):
- lââ¼[f]p = â¼â¨(λg,p. proj_path g (lâp)), f, pâ©.
-#f #p #l
->unwind_lcons_alt <unwind_path_append_sn //
-qed.
-
-lemma unwind_path_L_sn (f) (p):
- (ðââ¼[⫯f]p) = â¼[f](ðâp).
-// qed.
-
-lemma unwind_path_A_sn (f) (p):
- (ðââ¼[f]p) = â¼[f](ðâp).
-// qed.
-
-lemma unwind_path_S_sn (f) (p):
- (ð¦ââ¼[f]p) = â¼[f](ð¦âp).
-// qed.
-
-lemma unwind_path_after (p) (f1) (f2):
- â¼[f2]â¼[f1]p = â¼[f2âf1]p.
-#p @(path_ind_unwind ⦠p) -p // [ #n #l #p | #p ] #IH #f1 #f2
-[ <unwind_path_d_lcons_sn <unwind_path_d_lcons_sn
- >(unwind_path_eq_repl ⦠(tr_compose_assoc â¦)) //
-| <unwind_path_L_sn <unwind_path_L_sn <unwind_path_L_sn
- >tr_compose_push_bi //
-]
-qed.
-
-(* Advanced constructions with proj_rmap and stream_tls *********************)
-
-lemma unwind_rmap_tls_d_dx (f) (p) (m) (n):
- â*[m+n]â¼[p]f â â*[m]â¼[pâð±n]f.
-#f #p #m #n
-<unwind_rmap_d_dx >nrplus_inj_dx
-/2 width=1 by tr_tls_compose_uni_dx/
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_fsubst.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_fsubst.ma
deleted file mode 100644
index fedc665fb..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_fsubst.ma
+++ /dev/null
@@ -1,61 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind_prototerm_eq.ma".
-include "delayed_updating/unwind2/unwind_structure.ma".
-include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/syntax/preterm.ma".
-include "delayed_updating/syntax/prototerm_proper.ma".
-
-(* UNWIND FOR PROTOTERM *****************************************************)
-
-(* Constructions with fsubst ************************************************)
-
-lemma unwind_fsubst_sn (f) (t) (u) (p): u ϵ ð â
- (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u] â â¼[f](t[âpâu]).
-#f #t #u #p #Hu #ql * *
-[ #rl * #r #Hr #H1 #H2 destruct
- >unwind_append_proper_dx
- /4 width=5 by in_comp_unwind_bi, in_ppc_comp_trans, or_introl, ex2_intro/
-| * #q #Hq #H1 #H0
- @(ex2_intro ⦠H1) @or_intror @conj // *
- [ <list_append_empty_dx #H2 destruct
- elim (unwind_path_root f q) #r #_ #Hr /2 width=2 by/
- | #l #r #H2 destruct
- @H0 -H0 [| <unwind_append_proper_dx /2 width=3 by ppc_lcons/ ]
- ]
-]
-qed-.
-
-lemma unwind_fsubst_dx (f) (t) (u) (p): u ϵ ð â p ϵ âµt â t ϵ ð â
- â¼[f](t[âpâu]) â (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u].
-#f #t #u #p #Hu #H1p #H2p #ql * #q * *
-[ #r #Hu #H1 #H2 destruct
- @or_introl @ex2_intro
- [|| <unwind_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
- /2 width=3 by ex2_intro/
-| #Hq #H0 #H1 destruct
- @or_intror @conj [ /2 width=1 by in_comp_unwind_bi/ ] *
- [ <list_append_empty_dx #Hr @(H0 ⦠(ð)) -H0
- <list_append_empty_dx @H2p -H2p /2 width=1 by prototerm_in_comp_root/
- | #l #r #Hr
- elim (unwind_inv_append_proper_dx ⦠Hr) -Hr // #s1 #s2 #Hs1 #_ #H1 destruct
- lapply (H2p ⦠Hs1) -H2p -Hs1 /2 width=2 by ex_intro/
- ]
-]
-qed-.
-
-lemma unwind_fsubst (f) (t) (u) (p): u ϵ ð â p ϵ âµt â t ϵ ð â
- (â¼[f]t)[â(âp)ââ¼[â¼[p]f]u] â â¼[f](t[âpâu]).
-/4 width=3 by unwind_fsubst_sn, conj, unwind_fsubst_dx/ qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_height.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_height.ma
deleted file mode 100644
index d2678f61e..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_height.ma
+++ /dev/null
@@ -1,83 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind_eq.ma".
-include "delayed_updating/syntax/path_height.ma".
-include "delayed_updating/syntax/path_depth.ma".
-include "ground/lib/stream_eq_eq.ma".
-
-(* UNWIND FOR PATH **********************************************************)
-
-(* Constructions with height ************************************************)
-
-lemma unwind_rmap_pap_le (f1) (f2) (p) (m:pnat) (l:nat):
- ninj (m+⧣p+l) = âpâ â
- (â¼[p]f1)@â¨mâ© = (â¼[p]f2)@â¨mâ©.
-#f1 #f2 #p @(list_ind_rcons ⦠p) -p
-[ #m #l <depth_empty #H0 destruct
-| #p * [ #n ] #IH #m #l
- [ <height_d_dx <depth_d_dx <unwind_rmap_pap_d_dx <unwind_rmap_pap_d_dx
- <nplus_comm <nrplus_inj_sn <nrplus_inj_dx <nrplus_pplus_assoc
- #H0 <(IH ⦠l) -IH //
- | /2 width=2 by/
- | <height_L_dx <depth_L_dx <unwind_rmap_L_dx <unwind_rmap_L_dx
- cases m -m // #m
- <nrplus_succ_sn <nrplus_succ_sn >nsucc_inj #H0
- <tr_pap_push <tr_pap_push
- <(IH ⦠l) -IH //
- | /2 width=2 by/
- | /2 width=2 by/
- ]
-]
-qed.
-
-lemma unwind_rmap_pap_gt (f) (p) (m):
- f@â¨m+⧣pâ©+âpâ = (â¼[p]f)@â¨m+âpââ©.
-#f #p @(list_ind_rcons ⦠p) -p [ // ]
-#p * [ #n ] #IH #m
-[ <height_d_dx <depth_d_dx
- <nplus_comm <nrplus_inj_sn <nrplus_inj_dx <nrplus_pplus_assoc
- <unwind_rmap_pap_d_dx >IH -IH //
-| //
-| <height_L_dx <depth_L_dx
- <nrplus_succ_dx <nrplus_succ_dx <unwind_rmap_L_dx <tr_pap_push //
-| //
-| //
-]
-qed.
-
-lemma unwind_rmap_tls_gt (f) (p) (m:pnat):
- â*[ninj (m+⧣p)]f â â*[ninj (m+âpâ)]â¼[p]f.
-#f #p @(list_ind_rcons ⦠p) -p [ // ]
-#p * [ #n ] #IH #m
-[ <height_d_dx <depth_d_dx
- <nplus_comm <nrplus_inj_sn <nrplus_inj_dx <nrplus_pplus_assoc
- @(stream_eq_trans ⦠(unwind_rmap_tls_d_dx â¦))
- @(stream_eq_canc_dx ⦠(IH â¦)) -IH //
-| //
-| <height_L_dx <depth_L_dx
- <nrplus_succ_dx >nsucc_inj //
-| //
-| //
-]
-qed.
-
-lemma unwind_rmap_tls_eq (f) (p):
- â*[⧣p]f â â*[ââpâ]â¼[p]⫯f.
-(*
-#f #p @(list_ind_rcons ⦠p) -p //
-#p * [ #n ] #IH //
-<height_d_dx <depth_d_dx <unwind_rmap_d_dx
-@(stream_eq_trans ⦠(tr_tls_compose_uni_dx â¦))
-*)
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_preterm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_preterm_eq.ma
deleted file mode 100644
index d60c54cc6..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_preterm_eq.ma
+++ /dev/null
@@ -1,68 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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 "ground/lib/subset_equivalence.ma".
-include "delayed_updating/syntax/path_structure_inner.ma".
-include "delayed_updating/syntax/preterm.ma".
-include "delayed_updating/unwind2/unwind_structure.ma".
-include "delayed_updating/unwind2/unwind_prototerm.ma".
-
-(* UNWIND FOR PRETERM *******************************************************)
-
-(* Constructions with subset_equivalence ************************************)
-
-lemma unwind_grafted_sn (f) (t) (p): p ϵ ð â
- â¼[â¼[p]f](tâp) â (â¼[f]t)â(âp).
-#f #t #p #Hp #q * #r #Hr #H0 destruct
-@(ex2_intro ⦠Hr) -Hr
-<unwind_append_inner_sn //
-qed-.
-
-lemma unwind_grafted_dx (f) (t) (p): p ϵ ð â p ϵ âµt â t ϵ ð â
- (â¼[f]t)â(âp) â â¼[â¼[p]f](tâp).
-#f #t #p #H1p #H2p #Ht #q * #r #Hr #H0
-elim (unwind_inv_append_inner_sn ⦠(sym_eq ⦠H0)) -H0 //
-#p0 #q0 #Hp0 #Hq0 #H0 destruct
-<(Ht ⦠Hp0) [|*: /2 width=2 by ex_intro/ ] -p
-/2 width=1 by in_comp_unwind_bi/
-qed-.
-
-lemma unwind_grafted (f) (t) (p): p ϵ ð â p ϵ âµt â t ϵ ð â
- â¼[â¼[p]f](tâp) â (â¼[f]t)â(âp).
-/3 width=1 by unwind_grafted_sn, conj, unwind_grafted_dx/ qed.
-
-
-lemma unwind_grafted_S_dx (f) (t) (p): p ϵ âµt â t ϵ ð â
- (â¼[f]t)â((âp)âð¦) â â¼[â¼[p]f](tâ(pâð¦)).
-#f #t #p #Hp #Ht #q * #r #Hr
-<list_append_rcons_sn #H0
-elim (unwind_inv_append_proper_dx ⦠(sym_eq ⦠H0)) -H0 //
-#p0 #q0 #Hp0 #Hq0 #H0 destruct
-<(Ht ⦠Hp0) [|*: /2 width=2 by ex_intro/ ] -p
-elim (unwind_path_inv_S_sn ⦠(sym_eq ⦠Hq0)) -Hq0
-#r1 #r2 #Hr1 #Hr2 #H0 destruct
-lapply (preterm_in_root_append_inv_structure_empty_dx ⦠p0 ⦠Ht Hr1)
-[ /2 width=2 by ex_intro/ ] -Hr1 #Hr1 destruct
-/2 width=1 by in_comp_unwind_bi/
-qed-.
-
-lemma unwind_grafted_S (f) (t) (p): p ϵ âµt â t ϵ ð â
- â¼[â¼[p]f](tâ(pâð¦)) â (â¼[f]t)â((âp)âð¦).
-#f #t #p #Hp #Ht
-@conj
-[ >unwind_rmap_S_dx >structure_S_dx
- @unwind_grafted_sn //
-| /2 width=1 by unwind_grafted_S_dx/
-]
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_prototerm.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_prototerm.ma
deleted file mode 100644
index 1a5d46b77..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_prototerm.ma
+++ /dev/null
@@ -1,30 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind.ma".
-include "delayed_updating/syntax/prototerm.ma".
-include "ground/lib/subset_ext.ma".
-
-(* UNWIND FOR PROTOTERM *****************************************************)
-
-interpretation
- "unwind (prototerm)"
- 'BlackDownTriangle f t = (subset_ext_f1 ? ? (unwind_gen ? proj_path f) t).
-
-(* Basic constructions ******************************************************)
-
-lemma in_comp_unwind_bi (f) (p) (t):
- p ϵ t â â¼[f]p ϵ â¼[f]t.
-/2 width=1 by subset_in_ext_f1_dx/
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_prototerm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_prototerm_eq.ma
deleted file mode 100644
index 15b8cdb2c..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_prototerm_eq.ma
+++ /dev/null
@@ -1,40 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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 "ground/lib/subset_ext_equivalence.ma".
-include "delayed_updating/unwind2/unwind_eq.ma".
-include "delayed_updating/unwind2/unwind_prototerm.ma".
-
-(* UNWIND FOR PROTOTERM *****************************************************)
-
-(* Constructions with subset_equivalence ************************************)
-
-lemma unwind_term_eq_repl_sn (f1) (f2) (t):
- f1 â f2 â â¼[f1]t â â¼[f2]t.
-/3 width=1 by subset_equivalence_ext_f1_exteq, unwind_path_eq_repl/
-qed.
-
-lemma unwind_term_eq_repl_dx (f) (t1) (t2):
- t1 â t2 â â¼[f]t1 â â¼[f]t2.
-/2 width=1 by subset_equivalence_ext_f1_bi/
-qed.
-
-lemma unwind_term_after (f1) (f2) (t):
- â¼[f2]â¼[f1]t â â¼[f2âf1]t.
-#f1 #f2 #t @subset_eq_trans
-[
-| @subset_inclusion_ext_f1_compose
-| @subset_equivalence_ext_f1_exteq /2 width=5/
-]
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_structure.ma
deleted file mode 100644
index b5d92a577..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_structure.ma
+++ /dev/null
@@ -1,269 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind_eq.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/syntax/path_inner.ma".
-include "delayed_updating/syntax/path_proper.ma".
-include "ground/xoa/ex_4_2.ma".
-
-(* UNWIND FOR PATH **********************************************************)
-
-(* Basic constructions with structure ***************************************)
-
-lemma structure_unwind (p) (f):
- âp = ââ¼[f]p.
-#p @(path_ind_unwind ⦠p) -p // #p #IH #f
-<unwind_path_L_sn //
-qed.
-
-lemma unwind_structure (p) (f):
- âp = â¼[f]âp.
-#p @(path_ind_unwind ⦠p) -p //
-qed.
-
-(* Destructions with structure **********************************************)
-
-lemma unwind_des_structure (q) (p) (f):
- âq = â¼[f]p â âq = âp.
-// qed-.
-
-(* Constructions with proper condition for path *****************************)
-
-lemma unwind_append_proper_dx (p2) (p1) (f): p2 ϵ ð â
- (âp1)â(â¼[â¼[p1]f]p2) = â¼[f](p1âp2).
-#p2 #p1 @(path_ind_unwind ⦠p1) -p1 //
-[ #n | #n #l #p1 |*: #p1 ] #IH #f #Hp2
-[ elim (ppc_inv_lcons ⦠Hp2) -Hp2 #l #q #H destruct //
-| <unwind_path_d_lcons_sn <IH //
-| <unwind_path_m_sn <IH //
-| <unwind_path_L_sn <IH //
-| <unwind_path_A_sn <IH //
-| <unwind_path_S_sn <IH //
-]
-qed-.
-
-(* Constructions with inner condition for path ******************************)
-
-lemma unwind_append_inner_sn (p1) (p2) (f): p1 ϵ ð â
- (âp1)â(â¼[â¼[p1]f]p2) = â¼[f](p1âp2).
-#p1 @(list_ind_rcons ⦠p1) -p1 // #p1 *
-[ #n ] #_ #p2 #f #Hp1
-[ elim (pic_inv_d_dx ⦠Hp1)
-| <list_append_rcons_sn <unwind_append_proper_dx //
-| <list_append_rcons_sn <unwind_append_proper_dx //
- <structure_L_dx <list_append_rcons_sn //
-| <list_append_rcons_sn <unwind_append_proper_dx //
- <structure_A_dx <list_append_rcons_sn //
-| <list_append_rcons_sn <unwind_append_proper_dx //
- <structure_S_dx <list_append_rcons_sn //
-]
-qed-.
-
-(* Advanced constructions with proj_path ************************************)
-
-lemma unwind_path_d_empty_dx (n) (p) (f):
- (âp)âð±((â¼[p]f)@â¨nâ©) = â¼[f](pâð±n).
-#n #p #f <unwind_append_proper_dx //
-qed.
-
-lemma unwind_path_m_dx (p) (f):
- âp = â¼[f](pâðº).
-#p #f <unwind_append_proper_dx //
-qed.
-
-lemma unwind_path_L_dx (p) (f):
- (âp)âð = â¼[f](pâð).
-#p #f <unwind_append_proper_dx //
-qed.
-
-lemma unwind_path_A_dx (p) (f):
- (âp)âð = â¼[f](pâð).
-#p #f <unwind_append_proper_dx //
-qed.
-
-lemma unwind_path_S_dx (p) (f):
- (âp)âð¦ = â¼[f](pâð¦).
-#p #f <unwind_append_proper_dx //
-qed.
-
-lemma unwind_path_root (f) (p):
- ââr. ð = âr & âpâr = â¼[f]p.
-#f #p @(list_ind_rcons ⦠p) -p
-[ /2 width=3 by ex2_intro/
-| #p * [ #n ] /2 width=3 by ex2_intro/
-]
-qed-.
-
-(* Advanced inversions with proj_path ***************************************)
-
-lemma unwind_path_inv_d_sn (k) (q) (p) (f):
- (ð±kâq) = â¼[f]p â
- ââr,h. ð = âr & (â¼[r]f)@â¨hâ© = k & ð = q & râð±h = p.
-#k #q #p @(path_ind_unwind ⦠p) -p
-[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
-[ <unwind_path_empty #H destruct
-| <unwind_path_d_empty_sn #H destruct -IH
- /2 width=5 by ex4_2_intro/
-| <unwind_path_d_lcons_sn #H
- elim (IH ⦠H) -IH -H #r #h #Hr #Hh #Hq #Hp destruct
- /2 width=5 by ex4_2_intro/
-| <unwind_path_m_sn #H
- elim (IH ⦠H) -IH -H #r #h #Hr #Hh #Hq #Hp destruct
- /2 width=5 by ex4_2_intro/
-| <unwind_path_L_sn #H destruct
-| <unwind_path_A_sn #H destruct
-| <unwind_path_S_sn #H destruct
-]
-qed-.
-
-lemma unwind_path_inv_m_sn (q) (p) (f):
- (ðºâq) = â¼[f]p â â¥.
-#q #p @(path_ind_unwind ⦠p) -p
-[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
-[ <unwind_path_empty #H destruct
-| <unwind_path_d_empty_sn #H destruct
-| <unwind_path_d_lcons_sn #H /2 width=2 by/
-| <unwind_path_m_sn #H /2 width=2 by/
-| <unwind_path_L_sn #H destruct
-| <unwind_path_A_sn #H destruct
-| <unwind_path_S_sn #H destruct
-]
-qed-.
-
-lemma unwind_path_inv_L_sn (q) (p) (f):
- (ðâq) = â¼[f]p â
- ââr1,r2. ð = âr1 & q = â¼[⫯â¼[r1]f]r2 & r1âðâr2 = p.
-#q #p @(path_ind_unwind ⦠p) -p
-[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
-[ <unwind_path_empty #H destruct
-| <unwind_path_d_empty_sn #H destruct
-| <unwind_path_d_lcons_sn #H
- elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
- /2 width=5 by ex3_2_intro/
-| <unwind_path_m_sn #H
- elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
- /2 width=5 by ex3_2_intro/
-| <unwind_path_L_sn #H destruct -IH
- /2 width=5 by ex3_2_intro/
-| <unwind_path_A_sn #H destruct
-| <unwind_path_S_sn #H destruct
-]
-qed-.
-
-lemma unwind_path_inv_A_sn (q) (p) (f):
- (ðâq) = â¼[f]p â
- ââr1,r2. ð = âr1 & q = â¼[â¼[r1]f]r2 & r1âðâr2 = p.
-#q #p @(path_ind_unwind ⦠p) -p
-[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
-[ <unwind_path_empty #H destruct
-| <unwind_path_d_empty_sn #H destruct
-| <unwind_path_d_lcons_sn #H
- elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
- /2 width=5 by ex3_2_intro/
-| <unwind_path_m_sn #H
- elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
- /2 width=5 by ex3_2_intro/
-| <unwind_path_L_sn #H destruct
-| <unwind_path_A_sn #H destruct -IH
- /2 width=5 by ex3_2_intro/
-| <unwind_path_S_sn #H destruct
-]
-qed-.
-
-lemma unwind_path_inv_S_sn (q) (p) (f):
- (ð¦âq) = â¼[f]p â
- ââr1,r2. ð = âr1 & q = â¼[â¼[r1]f]r2 & r1âð¦âr2 = p.
-#q #p @(path_ind_unwind ⦠p) -p
-[| #n | #n #l #p |*: #p ] [|*: #IH ] #f
-[ <unwind_path_empty #H destruct
-| <unwind_path_d_empty_sn #H destruct
-| <unwind_path_d_lcons_sn #H
- elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
- /2 width=5 by ex3_2_intro/
-| <unwind_path_m_sn #H
- elim (IH ⦠H) -IH -H #r1 #r2 #Hr1 #Hq #Hp destruct
- /2 width=5 by ex3_2_intro/| <unwind_path_L_sn #H destruct
-| <unwind_path_A_sn #H destruct
-| <unwind_path_S_sn #H destruct -IH
- /2 width=5 by ex3_2_intro/
-]
-qed-.
-
-(* Inversions with proper condition for path ********************************)
-
-lemma unwind_inv_append_proper_dx (q2) (q1) (p) (f):
- q2 ϵ ð â q1âq2 = â¼[f]p â
- ââp1,p2. âp1 = q1 & â¼[â¼[p1]f]p2 = q2 & p1âp2 = p.
-#q2 #q1 elim q1 -q1
-[ #p #f #Hq2 <list_append_empty_sn #H destruct
- /2 width=5 by ex3_2_intro/
-| * [ #n1 ] #q1 #IH #p #f #Hq2 <list_append_lcons_sn #H
- [ elim (unwind_path_inv_d_sn ⦠H) -H #r1 #m1 #_ #_ #H0 #_ -IH
- elim (eq_inv_list_empty_append ⦠H0) -H0 #_ #H0 destruct
- elim Hq2 -Hq2 //
- | elim (unwind_path_inv_m_sn ⦠H)
- | elim (unwind_path_inv_L_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
- elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
- @(ex3_2_intro ⦠(r1âðâp1)) //
- <structure_append <Hr1 -Hr1 //
- | elim (unwind_path_inv_A_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
- elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
- @(ex3_2_intro ⦠(r1âðâp1)) //
- <structure_append <Hr1 -Hr1 //
- | elim (unwind_path_inv_S_sn ⦠H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
- elim (IH ⦠Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
- @(ex3_2_intro ⦠(r1âð¦âp1)) //
- <structure_append <Hr1 -Hr1 //
- ]
-]
-qed-.
-
-(* Inversions with inner condition for path *********************************)
-
-lemma unwind_inv_append_inner_sn (q1) (q2) (p) (f):
- q1 ϵ ð â q1âq2 = â¼[f]p â
- ââp1,p2. âp1 = q1 & â¼[â¼[p1]f]p2 = q2 & p1âp2 = p.
-#q1 @(list_ind_rcons ⦠q1) -q1
-[ #q2 #p #f #Hq1 <list_append_empty_sn #H destruct
- /2 width=5 by ex3_2_intro/
-| #q1 * [ #n1 ] #_ #q2 #p #f #Hq2
- [ elim (pic_inv_d_dx ⦠Hq2)
- | <list_append_rcons_sn #H0
- elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
- elim (unwind_path_inv_m_sn ⦠(sym_eq ⦠H2))
- | <list_append_rcons_sn #H0
- elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
- elim (unwind_path_inv_L_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
- @(ex3_2_intro ⦠(p1âr2âð)) [1,3: // ]
- [ <structure_append <structure_L_dx <Hr2 -Hr2 //
- | <list_append_assoc <list_append_rcons_sn //
- ]
- | <list_append_rcons_sn #H0
- elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
- elim (unwind_path_inv_A_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
- @(ex3_2_intro ⦠(p1âr2âð)) [1,3: // ]
- [ <structure_append <structure_A_dx <Hr2 -Hr2 //
- | <list_append_assoc <list_append_rcons_sn //
- ]
- | <list_append_rcons_sn #H0
- elim (unwind_inv_append_proper_dx ⦠H0) -H0 // #p1 #p2 #H1 #H2 #H3 destruct
- elim (unwind_path_inv_S_sn ⦠(sym_eq ⦠H2)) -H2 #r2 #s2 #Hr2 #Hs2 #H0 destruct
- @(ex3_2_intro ⦠(p1âr2âð¦)) [1,3: // ]
- [ <structure_append <structure_S_dx <Hr2 -Hr2 //
- | <list_append_assoc <list_append_rcons_sn //
- ]
- ]
-]
-qed-.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_structure_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_structure_depth.ma
deleted file mode 100644
index 577a95bba..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind2/unwind_structure_depth.ma
+++ /dev/null
@@ -1,31 +0,0 @@
-(**************************************************************************)
-(* ___ *)
-(* ||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/unwind2/unwind.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/syntax/path_depth.ma".
-include "ground/arith/nat_pred_succ.ma".
-
-(* UNWIND FOR PATH **********************************************************)
-
-(* Basic constructions with structure and depth *****************************)
-
-lemma unwind_rmap_structure (p) (f):
- (⫯*[âpâ]f) = â¼[âp]f.
-#p elim p -p //
-* [ #n ] #p #IH #f //
-[ <unwind_rmap_A_sn //
-| <unwind_rmap_S_sn //
-]
-qed.