From 2e97c767bc072f5ba238725ff1f738fc91a0135a Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <fguidi@maelstrom.helm.cs.unibo.it>
Date: Thu, 10 Feb 2022 11:38:29 +0100
Subject: [PATCH] update in delayed_updating

+ relationship between grafted trees and updating clarified in the case of interest so far
---
 .../delayed_updating/reduction/dfr_ifr.ma     |  8 +++-
 .../substitution/lift_preterm_eq.ma           | 48 +++++++++----------
 .../ground/lib/subset_equivalence.ma          |  8 ++++
 3 files changed, 37 insertions(+), 27 deletions(-)

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
index 66affad94..839b4fdfa 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -16,7 +16,8 @@ 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".
-include "delayed_updating/substitution/lift_constructors.ma". 
+include "delayed_updating/substitution/lift_constructors.ma".
+include "delayed_updating/substitution/lift_preterm_eq.ma".
 include "delayed_updating/substitution/lift_structure_depth.ma".
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
@@ -40,6 +41,11 @@ lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
   [ <structure_append <structure_A_sn <structure_append <structure_L_sn
     @fsubst_eq_repl [ // ]
     @(subset_eq_trans … (lift_iref …))
+    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+    [ @lift_grafted_S /2 width=2 by ex_intro/ | skip ]
+    @(subset_eq_trans … (lift_term_after …))
+    @(subset_eq_canc_dx … (lift_term_after …))
+    @lift_term_eq_repl_sn -t1
   | //
   | /2 width=2 by ex_intro/
   | //
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma
index 8143f8600..d2bbd15be 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma
@@ -55,31 +55,27 @@ lemma lift_grafted (f) (t) (p): p ϵ 𝐈 → p ϵ ▵t → t ϵ 𝐓 →
       ↑[↑[p]f](t⋔p) ⇔ (↑[f]t)⋔(⊗p).
 /3 width=1 by lift_grafted_sn, conj, lift_grafted_dx/ qed.
 
-(*
 
--lemma lift_grafted_S_dx (f) (t) (p): p ϵ ▵t → t ϵ ������ →
--      (↑[f]t)⋔((⊗p)◖������) ⊆ ↑[↑[p]f](t⋔(p◖������)).
--#f #t #p #Hp #Ht #q * #r #Hr
--<list_append_rcons_sn #H0
--elim (lift_inv_append_proper_dx … (sym_eq … H0)) -H0 //
-+lemma lift_grafted_dx (f) (t) (p): p ϵ ������ → p ϵ ▵t → t ϵ ������ →
-+      (↑[f]t)⋔(⊗p) ⊆ ↑[↑[p]f](t⋔p).
-+#f #t #p #H1p #H2p #Ht #q * #r #Hr #H0
-+elim (lift_inv_append_inner_sn … (sym_eq … H0)) -H0 //
- #p0 #q0 #Hp0 #Hq0 #H0 destruct
- <(Ht … Hp0) [|*: /2 width=2 by ex_intro/ ] -p
--elim (lift_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_lift_bi/
- qed-.
- 
--lemma lift_grafted_S (f) (t) (p): p ϵ ▵t → t ϵ ������ →
--      ↑[↑[p]f](t⋔(p◖������)) ⇔ (↑[f]t)⋔((⊗p)◖������).
--/3 width=1 by lift_grafted_S_sn, conj, lift_grafted_S_dx/ qed.
-+lemma lift_grafted (f) (t) (p): p ϵ ������ → p ϵ ▵t → t ϵ ������ →
-+      ↑[↑[p]f](t⋔p) ⇔ (↑[f]t)⋔(⊗p).
-+/3 width=1 by lift_grafted_sn, conj, lift_grafted_dx/ qed.
+lemma lift_grafted_S_dx (f) (t) (p): p ϵ ▵t → t ϵ 𝐓 →
+      (↑[f]t)⋔((⊗p)◖𝗦) ⊆ ↑[↑[p]f](t⋔(p◖𝗦)).
+#f #t #p #Hp #Ht #q * #r #Hr
+<list_append_rcons_sn #H0
+elim (lift_inv_append_proper_dx … (sym_eq … H0)) -H0 //
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+<(Ht … Hp0) [|*: /2 width=2 by ex_intro/ ] -p
+elim (lift_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_lift_bi/
+qed-.
 
-*)
+lemma lift_grafted_S (f) (t) (p): p ϵ ▵t → t ϵ 𝐓 →
+      ↑[↑[p]f](t⋔(p◖𝗦)) ⇔ (↑[f]t)⋔((⊗p)◖𝗦).
+#f #t #p #Hp #Ht
+@conj
+[ >lift_rmap_S_dx >structure_S_dx
+  @lift_grafted_sn //
+| /2 width=1 by lift_grafted_S_dx/
+]
+qed.
diff --git a/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma b/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma
index cddb51e89..622ee0f55 100644
--- a/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/subset_equivalence.ma
@@ -56,3 +56,11 @@ theorem subset_eq_trans (A):
 #A #u1 #u2 * #H12 #H21 #u3 * #H23 #H32
 /3 width=5 by subset_le_trans, conj/
 qed-.
+
+theorem subset_eq_canc_sn (A):
+        left_cancellable … (subset_eq A).
+/3 width=3 by subset_eq_trans, subset_eq_sym/ qed-.
+
+theorem subset_eq_canc_dx (A):
+        right_cancellable … (subset_eq A).
+/3 width=3 by subset_eq_trans, subset_eq_sym/ qed-.
-- 
2.39.2