From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Thu, 23 Jun 2022 10:54:36 +0000 (+0200)
Subject: update in delayed_updating
X-Git-Tag: make_still_working~55
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=a4cacf8e269910184348a037106551dbc8a46fd4;p=helm.git
update in delayed_updating
+ unwind2_path_after_lift
+ prelift
+ refactoring for lift
---
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
index 9fbf809b3..f71d6974e 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
@@ -13,7 +13,6 @@
(**************************************************************************)
include "delayed_updating/reduction/dfr.ma".
-include "delayed_updating/reduction/ifr.ma".
include "delayed_updating/substitution/fsubst_lift.ma".
include "delayed_updating/substitution/fsubst_eq.ma".
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
new file mode 100644
index 000000000..6d5cb47f0
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
@@ -0,0 +1,55 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/reduction/ifr.ma".
+
+include "delayed_updating/unwind/unwind2_path_lift.ma".
+
+include "delayed_updating/substitution/fsubst_lift.ma".
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
+include "delayed_updating/substitution/lift_path_head.ma".
+include "delayed_updating/substitution/lift_rmap_head.ma".
+
+(* IMMEDIATE FOCUSED REDUCTION **********************************************)
+
+(* Constructions with lift **************************************************)
+
+theorem ifr_lift_bi (f) (p) (q) (t1) (t2):
+ t1 â¡ð¢ð[p,q] t2 â â[f]t1 â¡ð¢ð[â[f]p,â[â[pâðâð]f]q] â[f]t2.
+#f #p #q #t1 #t2
+* #n * #H1n #Ht1 #Ht2
+@(ex_intro ⦠((â[pâðâðâq]f)ï¼ â§£â¨nâ©)) @and3_intro
+[ -Ht1 -Ht2
+ <lift_rmap_L_dx >lift_path_L_sn
+ >list_append_rcons_sn in H1n; <reverse_append #H1n
+ <(lift_path_head ⦠H1n) -H1n //
+| lapply (in_comp_lift_path_term f ⦠Ht1) -Ht2 -Ht1 -H1n
+ <lift_path_d_dx #Ht1 //
+| lapply (lift_term_eq_repl_dx f ⦠Ht2) -Ht2 #Ht2 -Ht1
+ @(subset_eq_trans ⦠Ht2) -t2
+ @(subset_eq_trans ⦠(lift_term_fsubst â¦))
+ @fsubst_eq_repl [ // | <lift_path_append // ]
+(*
+ @(subset_eq_trans ⦠(lift_term_iref â¦))
+ @iref_eq_repl
+ @(subset_eq_canc_sn ⦠(lift_term_grafted_S â¦))
+ @lift_term_eq_repl_sn
+(* Note: crux of the proof begins *)
+ >list_append_rcons_sn in H1n; #H1n >lift_rmap_A_dx
+ /2 width=1 by tls_lift_rmap_append_closed/
+(* Note: crux of the proof ends *)
+]
+qed.
+*)
\ No newline at end of file
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
deleted file mode 100644
index b873ed303..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ /dev/null
@@ -1,150 +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/notation/functions/uparrow_4.ma".
-include "delayed_updating/notation/functions/uparrow_2.ma".
-include "delayed_updating/syntax/path.ma".
-include "ground/relocation/tr_uni.ma".
-include "ground/relocation/tr_pap_tls.ma".
-
-(* LIFT FOR PATH ************************************************************)
-
-definition lift_continuation (A:Type[0]) â
- tr_map â path â A.
-
-rec definition lift_gen (A:Type[0]) (k:lift_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 lift_gen (A) (λg,p. k g (ð±(fï¼ â§£â¨nâ©)âp)) (â*[n]f) q
- | label_m â lift_gen (A) (λg,p. k g (ðºâp)) f q
- | label_L â lift_gen (A) (λg,p. k g (ðâp)) (⫯f) q
- | label_A â lift_gen (A) (λg,p. k g (ðâp)) f q
- | label_S â lift_gen (A) (λg,p. k g (ð¦âp)) f q
- ]
-].
-
-interpretation
- "lift (gneric)"
- 'UpArrow A k f p = (lift_gen A k f p).
-
-definition proj_path: lift_continuation ⦠â
- λf,p.p.
-
-definition proj_rmap: lift_continuation ⦠â
- λf,p.f.
-
-interpretation
- "lift (path)"
- 'UpArrow f p = (lift_gen ? proj_path f p).
-
-interpretation
- "lift (relocation map)"
- 'UpArrow p f = (lift_gen ? proj_rmap f p).
-
-(* Basic constructions ******************************************************)
-
-lemma lift_empty (A) (k) (f):
- k f (ð) = â{A}â¨k, f, ðâ©.
-// qed.
-
-lemma lift_d_sn (A) (k) (p) (n) (f):
- ââ¨(λg,p. k g (ð±(fï¼ â§£â¨nâ©)âp)), â*[n]f, pâ© = â{A}â¨k, f, ð±nâpâ©.
-// qed.
-
-lemma lift_m_sn (A) (k) (p) (f):
- ââ¨(λg,p. k g (ðºâp)), f, pâ© = â{A}â¨k, f, ðºâpâ©.
-// qed.
-
-lemma lift_L_sn (A) (k) (p) (f):
- ââ¨(λg,p. k g (ðâp)), ⫯f, pâ© = â{A}â¨k, f, ðâpâ©.
-// qed.
-
-lemma lift_A_sn (A) (k) (p) (f):
- ââ¨(λg,p. k g (ðâp)), f, pâ© = â{A}â¨k, f, ðâpâ©.
-// qed.
-
-lemma lift_S_sn (A) (k) (p) (f):
- ââ¨(λg,p. k g (ð¦âp)), f, pâ© = â{A}â¨k, f, ð¦âpâ©.
-// qed.
-
-(* Basic constructions with proj_path ***************************************)
-
-lemma lift_path_empty (f):
- (ð) = â[f]ð.
-// qed.
-
-(* Basic constructions with proj_rmap ***************************************)
-
-lemma lift_rmap_empty (f):
- f = â[ð]f.
-// qed.
-
-lemma lift_rmap_d_sn (f) (p) (n):
- â[p](â*[ninj n]f) = â[ð±nâp]f.
-// qed.
-
-lemma lift_rmap_m_sn (f) (p):
- â[p]f = â[ðºâp]f.
-// qed.
-
-lemma lift_rmap_L_sn (f) (p):
- â[p](⫯f) = â[ðâp]f.
-// qed.
-
-lemma lift_rmap_A_sn (f) (p):
- â[p]f = â[ðâp]f.
-// qed.
-
-lemma lift_rmap_S_sn (f) (p):
- â[p]f = â[ð¦âp]f.
-// qed.
-
-(* Advanced constructions with proj_rmap and path_append ********************)
-
-lemma lift_rmap_append (p2) (p1) (f):
- â[p2]â[p1]f = â[p1âp2]f.
-#p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
-[ <lift_rmap_m_sn <lift_rmap_m_sn //
-| <lift_rmap_A_sn <lift_rmap_A_sn //
-| <lift_rmap_S_sn <lift_rmap_S_sn //
-]
-qed.
-
-(* Advanced constructions with proj_rmap and path_rcons *********************)
-
-lemma lift_rmap_d_dx (f) (p) (n):
- â*[ninj n](â[p]f) = â[pâð±n]f.
-// qed.
-
-lemma lift_rmap_m_dx (f) (p):
- â[p]f = â[pâðº]f.
-// qed.
-
-lemma lift_rmap_L_dx (f) (p):
- (⫯â[p]f) = â[pâð]f.
-// qed.
-
-lemma lift_rmap_A_dx (f) (p):
- â[p]f = â[pâð]f.
-// qed.
-
-lemma lift_rmap_S_dx (f) (p):
- â[p]f = â[pâð¦]f.
-// qed.
-
-lemma lift_rmap_pap_d_dx (f) (p) (n) (m):
- â[p]fï¼ â§£â¨m+nâ© = â[pâð±n]fï¼ â§£â¨mâ©+â[p]fï¼ â§£â¨nâ©.
-// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
deleted file mode 100644
index 317e1f424..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
+++ /dev/null
@@ -1,304 +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.ma".
-include "ground/relocation/tr_pap_pap.ma".
-include "ground/relocation/tr_pap_eq.ma".
-include "ground/relocation/tr_pn_eq.ma".
-include "ground/lib/stream_tls_plus.ma".
-include "ground/lib/stream_tls_eq.ma".
-include "ground/arith/nat_plus_rplus.ma".
-include "ground/arith/nat_rplus_pplus.ma".
-
-(* LIFT FOR PATH ************************************************************)
-
-definition lift_exteq (A): relation2 (lift_continuation A) (lift_continuation A) â
- λk1,k2. âf1,f2,p. f1 â f2 â k1 f1 p = k2 f2 p.
-
-interpretation
- "extensional equivalence (lift continuation)"
- 'RingEq A k1 k2 = (lift_exteq A k1 k2).
-
-(* Constructions with lift_exteq ********************************************)
-
-lemma lift_eq_repl (A) (p) (k1) (k2):
- k1 â{A} k2 â stream_eq_repl ⦠(λf1,f2. ââ¨k1, f1, pâ© = ââ¨k2, f2, pâ©).
-#A #p elim p -p [| * [ #n ] #q #IH ]
-#k1 #k2 #Hk #f1 #f2 #Hf
-[ <lift_empty <lift_empty /2 width=1 by/
-| <lift_d_sn <lift_d_sn <(tr_pap_eq_repl ⦠Hf)
- /3 width=3 by stream_tls_eq_repl, compose_repl_fwd_sn/
-| /3 width=1 by/
-| /3 width=1 by tr_push_eq_repl/
-| /3 width=1 by/
-| /3 width=1 by/
-]
-qed-.
-
-(* Advanced constructions ***************************************************)
-
-lemma lift_lcons_alt (A) (k) (f) (p) (l): k â k â
- ââ¨Î»g,p2. k g (lâp2), f, pâ© = â{A}â¨Î»g,p2. k g ((lâð)âp2), f, pâ©.
-#A #k #f #p #l #Hk
-@lift_eq_repl // #g1 #g2 #p2 #Hg @Hk -Hk // (**) (* auto fail *)
-qed.
-
-lemma lift_append_rcons_sn (A) (k) (f) (p1) (p) (l): k â k â
- ââ¨Î»g,p2. k g (p1âlâp2), f, pâ© = â{A}â¨Î»g,p2. k g (p1âlâp2), f, pâ©.
-#A #k #f #p1 #p #l #Hk
-@lift_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 lift_path_eq_repl (p):
- stream_eq_repl ⦠(λf1,f2. â[f1]p = â[f2]p).
-/2 width=1 by lift_eq_repl/ qed.
-
-lemma lift_path_append_sn (p) (f) (q):
- qââ[f]p = ââ¨(λg,p. proj_path g (qâp)), f, pâ©.
-#p elim p -p // * [ #n ] #p #IH #f #q
-[ <lift_d_sn <lift_d_sn
-| <lift_m_sn <lift_m_sn
-| <lift_L_sn <lift_L_sn
-| <lift_A_sn <lift_A_sn
-| <lift_S_sn <lift_S_sn
-]
->lift_lcons_alt // >lift_append_rcons_sn //
-<IH <IH -IH <list_append_rcons_sn //
-qed.
-
-lemma lift_path_lcons (f) (p) (l):
- lââ[f]p = ââ¨(λg,p. proj_path g (lâp)), f, pâ©.
-#f #p #l
->lift_lcons_alt <lift_path_append_sn //
-qed.
-
-lemma lift_path_d_sn (f) (p) (n):
- (ð±(fï¼ â§£â¨nâ©)ââ[â*[n]f]p) = â[f](ð±nâp).
-// qed.
-
-lemma lift_path_m_sn (f) (p):
- (ðºââ[f]p) = â[f](ðºâp).
-// qed.
-
-lemma lift_path_L_sn (f) (p):
- (ðââ[⫯f]p) = â[f](ðâp).
-// qed.
-
-lemma lift_path_A_sn (f) (p):
- (ðââ[f]p) = â[f](ðâp).
-// qed.
-
-lemma lift_path_S_sn (f) (p):
- (ð¦ââ[f]p) = â[f](ð¦âp).
-// qed.
-
-lemma lift_path_append (p2) (p1) (f):
- (â[f]p1)â(â[â[p1]f]p2) = â[f](p1âp2).
-#p2 #p1 elim p1 -p1 //
-* [ #n1 ] #p1 #IH #f
-[ <lift_path_d_sn <lift_path_d_sn <IH //
-| <lift_path_m_sn <lift_path_m_sn <IH //
-| <lift_path_L_sn <lift_path_L_sn <IH //
-| <lift_path_A_sn <lift_path_A_sn <IH //
-| <lift_path_S_sn <lift_path_S_sn <IH //
-]
-qed.
-
-lemma lift_path_d_dx (f) (p) (n):
- (â[f]p)âð±((â[p]f)ï¼ â§£â¨nâ©) = â[f](pâð±n).
-#f #p #n <lift_path_append //
-qed.
-
-lemma lift_path_m_dx (f) (p):
- (â[f]p)âðº = â[f](pâðº).
-#f #p <lift_path_append //
-qed.
-
-lemma lift_path_L_dx (f) (p):
- (â[f]p)âð = â[f](pâð).
-#f #p <lift_path_append //
-qed.
-
-lemma lift_path_A_dx (f) (p):
- (â[f]p)âð = â[f](pâð).
-#f #p <lift_path_append //
-qed.
-
-lemma lift_path_S_dx (f) (p):
- (â[f]p)âð¦ = â[f](pâð¦).
-#f #p <lift_path_append //
-qed.
-
-(* Advanced constructions with proj_rmap ************************************)
-
-lemma lift_rmap_eq_repl (p):
- stream_eq_repl ⦠(λf1,f2. â[p]f1 â â[p]f2).
-#p elim p -p //
-* [ #n ] #p #IH #f1 #f2 #Hf
-[ /3 width=1 by stream_tls_eq_repl/
-| /2 width=1 by/
-| /3 width=1 by tr_push_eq_repl/
-| /2 width=1 by/
-| /2 width=1 by/
-]
-qed.
-
-lemma tls_lift_rmap_d_dx (f) (p) (m) (n):
- â*[m+n]â[p]f â â*[m]â[pâð±n]f.
-#f #p #m #n
-<lift_rmap_d_dx >nrplus_inj_dx >nrplus_inj_sn //
-qed.
-
-(* Advanced inversions with proj_path ***************************************)
-
-lemma lift_path_inv_empty (f) (p):
- (ð) = â[f]p â ð = p.
-#f * // * [ #n ] #p
-[ <lift_path_d_sn
-| <lift_path_m_sn
-| <lift_path_L_sn
-| <lift_path_A_sn
-| <lift_path_S_sn
-] #H destruct
-qed-.
-
-lemma lift_path_inv_d_sn (f) (p) (q) (k):
- (ð±kâq) = â[f]p â
- ââr,h. k = fï¼ â§£â¨hâ© & q = â[â*[h]f]r & ð±hâr = p.
-#f * [| * [ #n ] #p ] #q #k
-[ <lift_path_empty
-| <lift_path_d_sn
-| <lift_path_m_sn
-| <lift_path_L_sn
-| <lift_path_A_sn
-| <lift_path_S_sn
-] #H destruct
-/2 width=5 by ex3_2_intro/
-qed-.
-
-lemma lift_path_inv_m_sn (f) (p) (q):
- (ðºâq) = â[f]p â
- ââr. q = â[f]r & ðºâr = p.
-#f * [| * [ #n ] #p ] #q
-[ <lift_path_empty
-| <lift_path_d_sn
-| <lift_path_m_sn
-| <lift_path_L_sn
-| <lift_path_A_sn
-| <lift_path_S_sn
-] #H destruct
-/2 width=3 by ex2_intro/
-qed-.
-
-lemma lift_path_inv_L_sn (f) (p) (q):
- (ðâq) = â[f]p â
- ââr. q = â[⫯f]r & ðâr = p.
-#f * [| * [ #n ] #p ] #q
-[ <lift_path_empty
-| <lift_path_d_sn
-| <lift_path_m_sn
-| <lift_path_L_sn
-| <lift_path_A_sn
-| <lift_path_S_sn
-] #H destruct
-/2 width=3 by ex2_intro/
-qed-.
-
-lemma lift_path_inv_A_sn (f) (p) (q):
- (ðâq) = â[f]p â
- ââr. q = â[f]r & ðâr = p.
-#f * [| * [ #n ] #p ] #q
-[ <lift_path_empty
-| <lift_path_d_sn
-| <lift_path_m_sn
-| <lift_path_L_sn
-| <lift_path_A_sn
-| <lift_path_S_sn
-] #H destruct
-/2 width=3 by ex2_intro/
-qed-.
-
-lemma lift_path_inv_S_sn (f) (p) (q):
- (ð¦âq) = â[f]p â
- ââr. q = â[f]r & ð¦âr = p.
-#f * [| * [ #n ] #p ] #q
-[ <lift_path_empty
-| <lift_path_d_sn
-| <lift_path_m_sn
-| <lift_path_L_sn
-| <lift_path_A_sn
-| <lift_path_S_sn
-] #H destruct
-/2 width=3 by ex2_intro/
-qed-.
-
-lemma lift_path_inv_append_sn (q2) (q1) (p) (f):
- q1âq2 = â[f]p â
- ââp1,p2. q1 = â[f]p1 & q2 = â[â[p1]f]p2 & p1âp2 = p.
-#q2 #q1 elim q1 -q1
-[| * [ #n1 ] #q1 #IH ] #p #f
-[ <list_append_empty_sn #H0 destruct
- /2 width=5 by ex3_2_intro/
-| <list_append_lcons_sn #H0
- elim (lift_path_inv_d_sn ⦠H0) -H0 #r1 #m1 #H1 #H0 #H2 destruct
- elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
- /2 width=5 by ex3_2_intro/
-| <list_append_lcons_sn #H0
- elim (lift_path_inv_m_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
- elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
- /2 width=5 by ex3_2_intro/
-| <list_append_lcons_sn #H0
- elim (lift_path_inv_L_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
- elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
- /2 width=5 by ex3_2_intro/
-| <list_append_lcons_sn #H0
- elim (lift_path_inv_A_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
- elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
- /2 width=5 by ex3_2_intro/
-| <list_append_lcons_sn #H0
- elim (lift_path_inv_S_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
- elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
- /2 width=5 by ex3_2_intro/
-]
-qed-.
-
-(* Main inversions with proj_path *******************************************)
-
-theorem lift_path_inj (q:path) (p) (f):
- â[f]q = â[f]p â q = p.
-#q elim q -q [| * [ #k ] #q #IH ] #p #f
-[ <lift_path_empty #H0
- <(lift_path_inv_empty ⦠H0) -H0 //
-| <lift_path_d_sn #H0
- elim (lift_path_inv_d_sn ⦠H0) -H0 #r #h #H0
- >(tr_pap_inj ???? H0) -k [1,3: // ] #Hr #H0 destruct
-| <lift_path_m_sn #H0
- elim (lift_path_inv_m_sn ⦠H0) -H0 #r #Hr #H0 destruct
-| <lift_path_L_sn #H0
- elim (lift_path_inv_L_sn ⦠H0) -H0 #r #Hr #H0 destruct
-| <lift_path_A_sn #H0
- elim (lift_path_inv_A_sn ⦠H0) -H0 #r #Hr #H0 destruct
-| <lift_path_S_sn #H0
- elim (lift_path_inv_S_sn ⦠H0) -H0 #r #Hr #H0 destruct
-]
-<(IH ⦠Hr) -r -IH //
-qed-.
-
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_gen.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_gen.ma
new file mode 100644
index 000000000..b873ed303
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_gen.ma
@@ -0,0 +1,150 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/notation/functions/uparrow_4.ma".
+include "delayed_updating/notation/functions/uparrow_2.ma".
+include "delayed_updating/syntax/path.ma".
+include "ground/relocation/tr_uni.ma".
+include "ground/relocation/tr_pap_tls.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+definition lift_continuation (A:Type[0]) â
+ tr_map â path â A.
+
+rec definition lift_gen (A:Type[0]) (k:lift_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 lift_gen (A) (λg,p. k g (ð±(fï¼ â§£â¨nâ©)âp)) (â*[n]f) q
+ | label_m â lift_gen (A) (λg,p. k g (ðºâp)) f q
+ | label_L â lift_gen (A) (λg,p. k g (ðâp)) (⫯f) q
+ | label_A â lift_gen (A) (λg,p. k g (ðâp)) f q
+ | label_S â lift_gen (A) (λg,p. k g (ð¦âp)) f q
+ ]
+].
+
+interpretation
+ "lift (gneric)"
+ 'UpArrow A k f p = (lift_gen A k f p).
+
+definition proj_path: lift_continuation ⦠â
+ λf,p.p.
+
+definition proj_rmap: lift_continuation ⦠â
+ λf,p.f.
+
+interpretation
+ "lift (path)"
+ 'UpArrow f p = (lift_gen ? proj_path f p).
+
+interpretation
+ "lift (relocation map)"
+ 'UpArrow p f = (lift_gen ? proj_rmap f p).
+
+(* Basic constructions ******************************************************)
+
+lemma lift_empty (A) (k) (f):
+ k f (ð) = â{A}â¨k, f, ðâ©.
+// qed.
+
+lemma lift_d_sn (A) (k) (p) (n) (f):
+ ââ¨(λg,p. k g (ð±(fï¼ â§£â¨nâ©)âp)), â*[n]f, pâ© = â{A}â¨k, f, ð±nâpâ©.
+// qed.
+
+lemma lift_m_sn (A) (k) (p) (f):
+ ââ¨(λg,p. k g (ðºâp)), f, pâ© = â{A}â¨k, f, ðºâpâ©.
+// qed.
+
+lemma lift_L_sn (A) (k) (p) (f):
+ ââ¨(λg,p. k g (ðâp)), ⫯f, pâ© = â{A}â¨k, f, ðâpâ©.
+// qed.
+
+lemma lift_A_sn (A) (k) (p) (f):
+ ââ¨(λg,p. k g (ðâp)), f, pâ© = â{A}â¨k, f, ðâpâ©.
+// qed.
+
+lemma lift_S_sn (A) (k) (p) (f):
+ ââ¨(λg,p. k g (ð¦âp)), f, pâ© = â{A}â¨k, f, ð¦âpâ©.
+// qed.
+
+(* Basic constructions with proj_path ***************************************)
+
+lemma lift_path_empty (f):
+ (ð) = â[f]ð.
+// qed.
+
+(* Basic constructions with proj_rmap ***************************************)
+
+lemma lift_rmap_empty (f):
+ f = â[ð]f.
+// qed.
+
+lemma lift_rmap_d_sn (f) (p) (n):
+ â[p](â*[ninj n]f) = â[ð±nâp]f.
+// qed.
+
+lemma lift_rmap_m_sn (f) (p):
+ â[p]f = â[ðºâp]f.
+// qed.
+
+lemma lift_rmap_L_sn (f) (p):
+ â[p](⫯f) = â[ðâp]f.
+// qed.
+
+lemma lift_rmap_A_sn (f) (p):
+ â[p]f = â[ðâp]f.
+// qed.
+
+lemma lift_rmap_S_sn (f) (p):
+ â[p]f = â[ð¦âp]f.
+// qed.
+
+(* Advanced constructions with proj_rmap and path_append ********************)
+
+lemma lift_rmap_append (p2) (p1) (f):
+ â[p2]â[p1]f = â[p1âp2]f.
+#p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
+[ <lift_rmap_m_sn <lift_rmap_m_sn //
+| <lift_rmap_A_sn <lift_rmap_A_sn //
+| <lift_rmap_S_sn <lift_rmap_S_sn //
+]
+qed.
+
+(* Advanced constructions with proj_rmap and path_rcons *********************)
+
+lemma lift_rmap_d_dx (f) (p) (n):
+ â*[ninj n](â[p]f) = â[pâð±n]f.
+// qed.
+
+lemma lift_rmap_m_dx (f) (p):
+ â[p]f = â[pâðº]f.
+// qed.
+
+lemma lift_rmap_L_dx (f) (p):
+ (⫯â[p]f) = â[pâð]f.
+// qed.
+
+lemma lift_rmap_A_dx (f) (p):
+ â[p]f = â[pâð]f.
+// qed.
+
+lemma lift_rmap_S_dx (f) (p):
+ â[p]f = â[pâð¦]f.
+// qed.
+
+lemma lift_rmap_pap_d_dx (f) (p) (n) (m):
+ â[p]fï¼ â§£â¨m+nâ© = â[pâð±n]fï¼ â§£â¨mâ©+â[p]fï¼ â§£â¨nâ©.
+// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_gen_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_gen_eq.ma
new file mode 100644
index 000000000..e589276a8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_gen_eq.ma
@@ -0,0 +1,304 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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_gen.ma".
+include "ground/relocation/tr_pap_pap.ma".
+include "ground/relocation/tr_pap_eq.ma".
+include "ground/relocation/tr_pn_eq.ma".
+include "ground/lib/stream_tls_plus.ma".
+include "ground/lib/stream_tls_eq.ma".
+include "ground/arith/nat_plus_rplus.ma".
+include "ground/arith/nat_rplus_pplus.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+definition lift_exteq (A): relation2 (lift_continuation A) (lift_continuation A) â
+ λk1,k2. âf1,f2,p. f1 â f2 â k1 f1 p = k2 f2 p.
+
+interpretation
+ "extensional equivalence (lift continuation)"
+ 'RingEq A k1 k2 = (lift_exteq A k1 k2).
+
+(* Constructions with lift_exteq ********************************************)
+
+lemma lift_eq_repl (A) (p) (k1) (k2):
+ k1 â{A} k2 â stream_eq_repl ⦠(λf1,f2. ââ¨k1, f1, pâ© = ââ¨k2, f2, pâ©).
+#A #p elim p -p [| * [ #n ] #q #IH ]
+#k1 #k2 #Hk #f1 #f2 #Hf
+[ <lift_empty <lift_empty /2 width=1 by/
+| <lift_d_sn <lift_d_sn <(tr_pap_eq_repl ⦠Hf)
+ /3 width=3 by stream_tls_eq_repl, compose_repl_fwd_sn/
+| /3 width=1 by/
+| /3 width=1 by tr_push_eq_repl/
+| /3 width=1 by/
+| /3 width=1 by/
+]
+qed-.
+
+(* Advanced constructions ***************************************************)
+
+lemma lift_lcons_alt (A) (k) (f) (p) (l): k â k â
+ ââ¨Î»g,p2. k g (lâp2), f, pâ© = â{A}â¨Î»g,p2. k g ((lâð)âp2), f, pâ©.
+#A #k #f #p #l #Hk
+@lift_eq_repl // #g1 #g2 #p2 #Hg @Hk -Hk // (**) (* auto fail *)
+qed.
+
+lemma lift_append_rcons_sn (A) (k) (f) (p1) (p) (l): k â k â
+ ââ¨Î»g,p2. k g (p1âlâp2), f, pâ© = â{A}â¨Î»g,p2. k g (p1âlâp2), f, pâ©.
+#A #k #f #p1 #p #l #Hk
+@lift_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 lift_path_eq_repl (p):
+ stream_eq_repl ⦠(λf1,f2. â[f1]p = â[f2]p).
+/2 width=1 by lift_eq_repl/ qed.
+
+lemma lift_path_append_sn (p) (f) (q):
+ qââ[f]p = ââ¨(λg,p. proj_path g (qâp)), f, pâ©.
+#p elim p -p // * [ #n ] #p #IH #f #q
+[ <lift_d_sn <lift_d_sn
+| <lift_m_sn <lift_m_sn
+| <lift_L_sn <lift_L_sn
+| <lift_A_sn <lift_A_sn
+| <lift_S_sn <lift_S_sn
+]
+>lift_lcons_alt // >lift_append_rcons_sn //
+<IH <IH -IH <list_append_rcons_sn //
+qed.
+
+lemma lift_path_lcons (f) (p) (l):
+ lââ[f]p = ââ¨(λg,p. proj_path g (lâp)), f, pâ©.
+#f #p #l
+>lift_lcons_alt <lift_path_append_sn //
+qed.
+
+lemma lift_path_d_sn (f) (p) (n):
+ (ð±(fï¼ â§£â¨nâ©)ââ[â*[n]f]p) = â[f](ð±nâp).
+// qed.
+
+lemma lift_path_m_sn (f) (p):
+ (ðºââ[f]p) = â[f](ðºâp).
+// qed.
+
+lemma lift_path_L_sn (f) (p):
+ (ðââ[⫯f]p) = â[f](ðâp).
+// qed.
+
+lemma lift_path_A_sn (f) (p):
+ (ðââ[f]p) = â[f](ðâp).
+// qed.
+
+lemma lift_path_S_sn (f) (p):
+ (ð¦ââ[f]p) = â[f](ð¦âp).
+// qed.
+
+lemma lift_path_append (p2) (p1) (f):
+ (â[f]p1)â(â[â[p1]f]p2) = â[f](p1âp2).
+#p2 #p1 elim p1 -p1 //
+* [ #n1 ] #p1 #IH #f
+[ <lift_path_d_sn <lift_path_d_sn <IH //
+| <lift_path_m_sn <lift_path_m_sn <IH //
+| <lift_path_L_sn <lift_path_L_sn <IH //
+| <lift_path_A_sn <lift_path_A_sn <IH //
+| <lift_path_S_sn <lift_path_S_sn <IH //
+]
+qed.
+
+lemma lift_path_d_dx (f) (p) (n):
+ (â[f]p)âð±((â[p]f)ï¼ â§£â¨nâ©) = â[f](pâð±n).
+#f #p #n <lift_path_append //
+qed.
+
+lemma lift_path_m_dx (f) (p):
+ (â[f]p)âðº = â[f](pâðº).
+#f #p <lift_path_append //
+qed.
+
+lemma lift_path_L_dx (f) (p):
+ (â[f]p)âð = â[f](pâð).
+#f #p <lift_path_append //
+qed.
+
+lemma lift_path_A_dx (f) (p):
+ (â[f]p)âð = â[f](pâð).
+#f #p <lift_path_append //
+qed.
+
+lemma lift_path_S_dx (f) (p):
+ (â[f]p)âð¦ = â[f](pâð¦).
+#f #p <lift_path_append //
+qed.
+
+(* Advanced constructions with proj_rmap ************************************)
+
+lemma lift_rmap_eq_repl (p):
+ stream_eq_repl ⦠(λf1,f2. â[p]f1 â â[p]f2).
+#p elim p -p //
+* [ #n ] #p #IH #f1 #f2 #Hf
+[ /3 width=1 by stream_tls_eq_repl/
+| /2 width=1 by/
+| /3 width=1 by tr_push_eq_repl/
+| /2 width=1 by/
+| /2 width=1 by/
+]
+qed.
+
+lemma tls_lift_rmap_d_dx (f) (p) (m) (n):
+ â*[m+n]â[p]f â â*[m]â[pâð±n]f.
+#f #p #m #n
+<lift_rmap_d_dx >nrplus_inj_dx >nrplus_inj_sn //
+qed.
+
+(* Advanced inversions with proj_path ***************************************)
+
+lemma lift_path_inv_empty (f) (p):
+ (ð) = â[f]p â ð = p.
+#f * // * [ #n ] #p
+[ <lift_path_d_sn
+| <lift_path_m_sn
+| <lift_path_L_sn
+| <lift_path_A_sn
+| <lift_path_S_sn
+] #H destruct
+qed-.
+
+lemma lift_path_inv_d_sn (f) (p) (q) (k):
+ (ð±kâq) = â[f]p â
+ ââr,h. k = fï¼ â§£â¨hâ© & q = â[â*[h]f]r & ð±hâr = p.
+#f * [| * [ #n ] #p ] #q #k
+[ <lift_path_empty
+| <lift_path_d_sn
+| <lift_path_m_sn
+| <lift_path_L_sn
+| <lift_path_A_sn
+| <lift_path_S_sn
+] #H destruct
+/2 width=5 by ex3_2_intro/
+qed-.
+
+lemma lift_path_inv_m_sn (f) (p) (q):
+ (ðºâq) = â[f]p â
+ ââr. q = â[f]r & ðºâr = p.
+#f * [| * [ #n ] #p ] #q
+[ <lift_path_empty
+| <lift_path_d_sn
+| <lift_path_m_sn
+| <lift_path_L_sn
+| <lift_path_A_sn
+| <lift_path_S_sn
+] #H destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma lift_path_inv_L_sn (f) (p) (q):
+ (ðâq) = â[f]p â
+ ââr. q = â[⫯f]r & ðâr = p.
+#f * [| * [ #n ] #p ] #q
+[ <lift_path_empty
+| <lift_path_d_sn
+| <lift_path_m_sn
+| <lift_path_L_sn
+| <lift_path_A_sn
+| <lift_path_S_sn
+] #H destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma lift_path_inv_A_sn (f) (p) (q):
+ (ðâq) = â[f]p â
+ ââr. q = â[f]r & ðâr = p.
+#f * [| * [ #n ] #p ] #q
+[ <lift_path_empty
+| <lift_path_d_sn
+| <lift_path_m_sn
+| <lift_path_L_sn
+| <lift_path_A_sn
+| <lift_path_S_sn
+] #H destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma lift_path_inv_S_sn (f) (p) (q):
+ (ð¦âq) = â[f]p â
+ ââr. q = â[f]r & ð¦âr = p.
+#f * [| * [ #n ] #p ] #q
+[ <lift_path_empty
+| <lift_path_d_sn
+| <lift_path_m_sn
+| <lift_path_L_sn
+| <lift_path_A_sn
+| <lift_path_S_sn
+] #H destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma lift_path_inv_append_sn (q2) (q1) (p) (f):
+ q1âq2 = â[f]p â
+ ââp1,p2. q1 = â[f]p1 & q2 = â[â[p1]f]p2 & p1âp2 = p.
+#q2 #q1 elim q1 -q1
+[| * [ #n1 ] #q1 #IH ] #p #f
+[ <list_append_empty_sn #H0 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_d_sn ⦠H0) -H0 #r1 #m1 #H1 #H0 #H2 destruct
+ elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_m_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_L_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_A_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_S_sn ⦠H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH ⦠H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+]
+qed-.
+
+(* Main inversions with proj_path *******************************************)
+
+theorem lift_path_inj (q:path) (p) (f):
+ â[f]q = â[f]p â q = p.
+#q elim q -q [| * [ #k ] #q #IH ] #p #f
+[ <lift_path_empty #H0
+ <(lift_path_inv_empty ⦠H0) -H0 //
+| <lift_path_d_sn #H0
+ elim (lift_path_inv_d_sn ⦠H0) -H0 #r #h #H0
+ >(tr_pap_inj ???? H0) -k [1,3: // ] #Hr #H0 destruct
+| <lift_path_m_sn #H0
+ elim (lift_path_inv_m_sn ⦠H0) -H0 #r #Hr #H0 destruct
+| <lift_path_L_sn #H0
+ elim (lift_path_inv_L_sn ⦠H0) -H0 #r #Hr #H0 destruct
+| <lift_path_A_sn #H0
+ elim (lift_path_inv_A_sn ⦠H0) -H0 #r #Hr #H0 destruct
+| <lift_path_S_sn #H0
+ elim (lift_path_inv_S_sn ⦠H0) -H0 #r #Hr #H0 destruct
+]
+<(IH ⦠Hr) -r -IH //
+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 c2376b52e..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_id.ma
+++ /dev/null
@@ -1,38 +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 proj_path and 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.
-
-(* Constructions with proj_rmap and tr_id ***********************************)
-
-lemma lift_rmap_id (p):
- (ð¢) = â[p]ð¢.
-#p elim p -p //
-* [ #n ] #p #IH //
-qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
index 869d680fe..1bdf3c592 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_gen_eq.ma".
include "ground/relocation/tr_compose_pap.ma".
include "ground/relocation/tr_compose_pn.ma".
include "ground/relocation/tr_compose_tls.ma".
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
index 71b11f5d6..772cc8d09 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_gen_eq.ma".
include "delayed_updating/syntax/path_head.ma".
include "delayed_updating/syntax/path_reverse.ma".
include "ground/relocation/xap.ma".
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma
new file mode 100644
index 000000000..cac770811
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma
@@ -0,0 +1,30 @@
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "delayed_updating/substitution/lift_gen_eq.ma".
+include "ground/relocation/tr_id_pap.ma".
+include "ground/relocation/tr_id_tls.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+(* Constructions with proj_path and 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_path_length.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma
index a4b81aeeb..755f8d16e 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_gen_eq.ma".
include "ground/lib/list_length.ma".
(* LIFT FOR PATH ************************************************************)
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_prelift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_prelift.ma
new file mode 100644
index 000000000..345f437ab
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_prelift.ma
@@ -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/substitution/lift_gen_eq.ma".
+include "delayed_updating/substitution/prelift_label.ma".
+include "delayed_updating/substitution/prelift_rmap.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+(* Constructions with prelift_rmap and prelift_path *************************)
+
+lemma lift_path_lcons_prelift (f) (p) (l):
+ (â[f]l)ââ[â[l]f]p = â[f](lâp).
+#f #p * [ #n ] //
+qed.
+
+lemma lift_path_rcons_prelift (f) (p) (l):
+ (â[f]p)ââ[â[p]f]l = â[f](pâl).
+#f #p * [ #n ] //
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma
index 0eef97896..1473e819f 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_proper.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_gen_eq.ma".
include "delayed_updating/syntax/path_proper.ma".
(* LIFT FOR PATH ************************************************************)
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma
index 773749b63..ece3e93e6 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_gen_eq.ma".
include "delayed_updating/syntax/path_structure.ma".
(* LIFT FOR PATH ************************************************************)
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
index 0e22a3d39..f68010b32 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_id.ma".
+include "delayed_updating/substitution/lift_path_id.ma".
include "ground/relocation/tr_uni_pap.ma".
include "ground/relocation/tr_uni_tls.ma".
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
index ed5fbe84c..85aa8a0bb 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift.ma".
+include "delayed_updating/substitution/lift_gen.ma".
include "delayed_updating/syntax/prototerm.ma".
include "ground/lib/subset_ext.ma".
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
index 7343319f4..11e39983b 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
@@ -13,7 +13,7 @@
(**************************************************************************)
include "delayed_updating/substitution/lift_prototerm_eq.ma".
-include "delayed_updating/substitution/lift_id.ma".
+include "delayed_updating/substitution/lift_path_id.ma".
(* LIFT FOR PROTOTERM *******************************************************)
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma
index 122262026..3dadf0fcd 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_head.ma
@@ -12,7 +12,7 @@
(* *)
(**************************************************************************)
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_gen_eq.ma".
include "delayed_updating/syntax/path_head.ma".
include "delayed_updating/syntax/path_reverse.ma".
include "ground/lib/stream_eq_eq.ma".
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
new file mode 100644
index 000000000..077f90747
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap_id.ma
@@ -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/substitution/lift_gen.ma".
+include "ground/relocation/tr_id_tls.ma".
+
+(* LIFT FOR RELOCATION MAP *************************************************)
+
+(* Constructions with proj_rmap and tr_id ***********************************)
+
+lemma lift_rmap_id (p):
+ (ð¢) = â[p]ð¢.
+#p elim p -p //
+* [ #n ] #p #IH //
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma
new file mode 100644
index 000000000..e4a9c0596
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma
@@ -0,0 +1,54 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/notation/functions/uparrow_2.ma".
+include "delayed_updating/syntax/label.ma".
+include "ground/relocation/tr_pap.ma".
+
+(* PRELIFT FOR LABEL ********************************************************)
+
+definition prelift_label (f) (l): label â
+match l with
+[ label_d n â ð±(fï¼ â§£â¨nâ©)
+| label_m â ðº
+| label_L â ð
+| label_A â ð
+| label_S â ð¦
+].
+
+interpretation
+ "prelift (label)"
+ 'UpArrow f l = (prelift_label f l).
+
+(* Basic constructions ******************************************************)
+
+lemma prelift_label_d (f) (n):
+ (ð±(fï¼ â§£â¨nâ©)) = â[f]ð±n.
+// qed.
+
+lemma prelift_label_m (f):
+ (ðº) = â[f]ðº.
+// qed.
+
+lemma prelift_label_L (f):
+ (ð) = â[f]ð.
+// qed.
+
+lemma prelift_label_A (f):
+ (ð) = â[f]ð.
+// qed.
+
+lemma prelift_label_S (f):
+ (ð¦) = â[f]ð¦.
+// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap.ma
new file mode 100644
index 000000000..de7f40321
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_rmap.ma
@@ -0,0 +1,55 @@
+(**************************************************************************)
+(* ___ *)
+(* ||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/notation/functions/uparrow_2.ma".
+include "delayed_updating/syntax/label.ma".
+include "ground/relocation/tr_pn.ma".
+include "ground/lib/stream_tls.ma".
+
+(* PRELIFT FOR RELOCATION MAP ***********************************************)
+
+definition prelift_rmap (f) (l): tr_map â
+match l with
+[ label_d n â â*[n]f
+| label_m â f
+| label_L â ⫯f
+| label_A â f
+| label_S â f
+].
+
+interpretation
+ "prelift (relocation map)"
+ 'UpArrow l f = (prelift_rmap f l).
+
+(* Basic constructions ******************************************************)
+
+lemma prelift_rmap_d (f) (n:pnat):
+ â*[n]f = â[ð±n]f.
+// qed.
+
+lemma prelift_rmap_m (f):
+ f = â[ðº]f.
+// qed.
+
+lemma prelift_rmap_L (f):
+ (⫯f) = â[ð]f.
+// qed.
+
+lemma prelift_rmap_A (f):
+ f = â[ð]f.
+// qed.
+
+lemma prelift_rmap_S (f):
+ f = â[ð¦]f.
+// qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
index 71a169dbf..ac2166a46 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_lift.ma
@@ -13,13 +13,13 @@
(**************************************************************************)
include "delayed_updating/unwind/unwind2_path_eq.ma".
-include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_path_prelift.ma".
(* UNWIND FOR PATH **********************************************************)
-(* Properties with lift_path ************************************************)
+(* Constructions with lift_path *********************************************)
-lemma unwind2_lift_path_after (p) (f1) (f2):
+lemma lift_unwind2_path_after (p) (f1) (f2):
â[f2]â¼[f1]p = â¼[f2âf1]p.
#p @(path_ind_unwind ⦠p) -p // [ #n | #p ] #IH #f1 #f2
[ <unwind2_path_d_empty <unwind2_path_d_empty
@@ -28,3 +28,19 @@ lemma unwind2_lift_path_after (p) (f1) (f2):
>tr_compose_push_bi //
]
qed.
+
+lemma unwind2_path_after_lift (p) (f1) (f2):
+ â¼[f2]â[f1]p = â¼[f2âf1]p.
+#p @(path_ind_unwind ⦠p) -p // [ #n #l ] #p #IH #f1 #f2
+[ <lift_path_d_sn <unwind2_path_d_lcons
+ <lift_path_lcons_prelift <unwind2_path_d_lcons >lift_path_lcons_prelift
+ >IH -IH
+ >(unwind2_path_eq_repl ⦠(tr_compose_assoc â¦))
+ >(unwind2_path_eq_repl ⦠(tr_compose_assoc â¦))
+ <unwind2_path_after <unwind2_path_after in ⢠(???%);
+ /3 width=1 by unwind2_path_eq_repl, eq_f/
+| <lift_path_m_sn <unwind2_path_m_sn <unwind2_path_m_sn //
+| <lift_path_L_sn <unwind2_path_L_sn <unwind2_path_L_sn
+ >tr_compose_push_bi //
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma
index 8e3d2cf2f..8d987dfb7 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_lift.ma
@@ -22,10 +22,18 @@ include "delayed_updating/unwind/unwind2_prototerm.ma".
(* Constructions with lift_prototerm ****************************************)
-lemma unwind2_lift_term_after (f1) (f2) (t):
+lemma lift_unwind2_term_after (f1) (f2) (t):
â[f2]â¼[f1]t â â¼[f2âf1]t.
#f1 #f2 #t @subset_eq_trans
[| @subset_inclusion_ext_f1_compose ]
@subset_equivalence_ext_f1_exteq #p
-@unwind2_lift_path_after
+@lift_unwind2_path_after
+qed.
+
+lemma unwind2_term_after_lift (f1) (f2) (t):
+ â¼[f2]â[f1]t â â¼[f2âf1]t.
+#f1 #f2 #t @subset_eq_trans
+[| @subset_inclusion_ext_f1_compose ]
+@subset_equivalence_ext_f1_exteq #p
+@unwind2_path_after_lift
qed.