update in delayed updating

+ additions to lift
+ bugs fixed in dtr and itr

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
index e118134dd450a7bfcc2a49c6865b250a62c90d05..42d9e0c76c14c11e14a509cf4b3f5434d7939ea9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
@@ -29,7 +29,7 @@ include "ground/xoa/and_4.ma".
 definition dfr (p) (q): relation2 prototerm prototerm ≝
            λt1,t2. ∃∃b,n.
            let r ≝ p●𝗔◗b●𝗟◗q in
-           ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]f)@❨n❩ & r◖𝗱n ϵ t1 &
+           ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
               t1[⋔r←𝛗(n+❘b❘).(t1⋔(p◖𝗦))] ⇔ t2
 .
 

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 c555072f6558176f3d9d046ffb611e37fcf778c0..9a376bed0e223b86f80c4284aecd5ba9a80f02c2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -32,7 +32,7 @@ lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
   >tr_pushs_swap <tr_pap_pushs_le //
 | lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
   <lift_d_empty_dx //
-| lapply (eq_lift_bi f … Ht2) -Ht2 #Ht2
+| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (lift_fsubst …))
   [ <structure_append <structure_A_sn <structure_append <structure_L_sn

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index 1371c3a31ddeda6c9d1b9b47768c1732110f1e6a..0ac73291f5939f64d1780ec308974adb7873ea1b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -14,6 +14,7 @@
 
 include "delayed_updating/substitution/fsubst.ma".
 include "delayed_updating/substitution/lift_prototerm.ma".
+include "delayed_updating/syntax/prototerm_equivalence.ma".
 include "delayed_updating/syntax/path_depth.ma".
 include "delayed_updating/syntax/path_structure.ma".
 include "delayed_updating/syntax/path_balanced.ma".
@@ -26,7 +27,7 @@ include "ground/xoa/and_4.ma".
 definition ifr (p) (q): relation2 prototerm prototerm ≝
            λt1,t2. ∃∃b,n.
            let r ≝ p●𝗔◗b●𝗟◗q in
-           ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]f)@❨n❩ & r◖𝗱n ϵ t1 &
+           ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
               t1[⋔r←↑[𝐮❨❘b●𝗟◗q❘❩](t1⋔(p◖𝗦))] ⇔ t2
 .
 

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
index 21186fdd65c6bbe0bdf65cd8fcc7ec25352cba76..c98698864fdb04ead636d08143cfc9dff5f65d1f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/fsubst_lift.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/substitution/lift_prototerm.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
 include "delayed_updating/substitution/lift_structure.ma".
 include "delayed_updating/syntax/preterm.ma".
 include "delayed_updating/syntax/prototerm_proper.ma".

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
index 6825b13aa3109a7765f5fcb12efe9b0594a5856b..89ef40e91fdcc9362a7e7f6bb04ddf9926ea0d08 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -12,31 +12,13 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/relocation/tr_compose_compose.ma".
-include "ground/relocation/tr_compose_pn.ma".
-include "delayed_updating/substitution/lift_eq.ma".
-
-lemma lift_path_after (p) (f1) (f2):
-      ↑[f2]↑[f1]p = ↑[f2∘f1]p.
-#p @(path_ind_lift … p) -p // [ #n #l #p | #p ] #IH #f1 #f2
-[ <lift_path_d_lcons_sn <lift_path_d_lcons_sn
-  >(lift_path_eq_repl … (tr_compose_assoc …)) //
-| <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
-  >tr_compose_push_bi //
-]
-qed.
-
-include "delayed_updating/substitution/lift_prototerm.ma".
-
-axiom lift_term_after (t) (f1) (f2):
-      ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]t.
-
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
 include "delayed_updating/syntax/prototerm_constructors.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
 
-lemma lift_iref_after_sn (f) (t) (n:pnat):
-      (↑[f∘𝐮❨n❩]t) ⊆ ↑[f](𝛗n.t).
+lemma lift_iref_after_sn (f) (t:prototerm) (n:pnat):
+      ↑[f∘𝐮❨n❩]t ⊆ ↑[f](𝛗n.t).
 #f #t #n #p * #q #Hq #H0 destruct
 @(ex2_intro … (𝗱n◗𝗺◗q))
 /2 width=1 by in_comp_iref/

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
index 9e23b2cb9a5620d08bab1658735ea0cc32344dd6..dc3000c1563f6a4d70c767aa8b195718a66b2d2a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
@@ -13,6 +13,8 @@
 (**************************************************************************)
 
 include "delayed_updating/substitution/lift.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".
 
@@ -99,3 +101,13 @@ lemma lift_path_A_sn (f) (p):
 lemma lift_path_S_sn (f) (p):
       (𝗦◗↑[f]p) = ↑[f](𝗦◗p).
 // qed.
+
+lemma lift_path_after (p) (f1) (f2):
+      ↑[f2]↑[f1]p = ↑[f2∘f1]p.
+#p @(path_ind_lift … p) -p // [ #n #l #p | #p ] #IH #f1 #f2
+[ <lift_path_d_lcons_sn <lift_path_d_lcons_sn
+  >(lift_path_eq_repl … (tr_compose_assoc …)) //
+| <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
+  >tr_compose_push_bi //
+]
+qed.

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 4a0615a3ca081265e256e54a4cb683ef7810e351..6555b5d9ed0ec36e6d6d1605a92cfe591e740a63 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm.ma
@@ -14,7 +14,7 @@
 
 include "delayed_updating/substitution/lift.ma".
 include "delayed_updating/syntax/prototerm.ma".
-include "ground/lib/subset_ext_equivalence.ma".
+include "ground/lib/subset_ext.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
 
@@ -28,8 +28,3 @@ lemma in_comp_lift_bi (f) (p) (t):
       p ϵ t → ↑[f]p ϵ ↑[f]t.
 /2 width=1 by subset_in_ext_f1_dx/
 qed.
-
-lemma eq_lift_bi (f) (t1) (t2):
-      t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
-/2 width=1 by subset_equivalence_ext_f1_bi/
-qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
new file mode 100644 (file)
index 0000000..44ec5a3
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
@@ -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/substitution/lift_eq.ma".
+include "delayed_updating/substitution/lift_prototerm.ma".
+
+(* LIFT FOR PROTOTERM *******************************************************)
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma lift_term_eq_repl_sn (f1) (f2) (t):
+      f1 ≗ f2 → ↑[f1]t ⇔ ↑[f2]t.
+/3 width=1 by subset_equivalence_ext_f1_exteq, lift_path_eq_repl/
+qed.
+
+lemma lift_term_eq_repl_dx (f) (t1) (t2):
+      t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
+/2 width=1 by subset_equivalence_ext_f1_bi/
+qed.
+
+lemma lift_term_after (f1) (f2) (t):
+      ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]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/substitution/lift_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
index b9bc27c54c98ea4b0ec0662163e51a1a3e26b1f6..449317ee611227f71ab9a742810bcc342988a31c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
@@ -16,7 +16,6 @@ include "delayed_updating/substitution/lift_eq.ma".
 include "delayed_updating/syntax/path_structure.ma".
 include "delayed_updating/syntax/path_proper.ma".
 include "ground/xoa/ex_4_2.ma".
-include "ground/xoa/ex_3_2.ma".
 
 (* LIFT FOR PATH ***********************************************************)