update in delayed_updating

+ lift changed to lift after unwind in ifr
+ notion of lift swapped again
+ some additions to prove a side condition of ifr_unwind_bi

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 8403b778197501e01535e3c42490548cd0181ac7..be7f3b3d3d3825973ccb0af6aa5360a0cbb7b7a2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -18,11 +18,9 @@ include "delayed_updating/reduction/ifr.ma".
 include "delayed_updating/unwind/unwind2_constructors.ma".
 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
-include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
 include "delayed_updating/unwind/unwind2_rmap_head.ma".
 
 include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
 
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
 include "delayed_updating/syntax/path_head_structure.ma".
@@ -38,12 +36,12 @@ theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
         t1 ➡𝐝𝐟[p,q] t2 → ▼[f]t1 ➡𝐟[⊗p,⊗q] ▼[f]t2.
 #f #p #q #t1 #t2 #H0t1
 * #n * #H1n #Ht1 #Ht2
-@(ex_intro … (↑♭⊗q)) @and3_intro
+@(ex_intro … (↑♭q)) @and3_intro
 [ -H0t1 -Ht1 -Ht2
   >structure_L_sn >structure_reverse
   >H1n >path_head_structure_depth <H1n -H1n //
 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
-  <unwind2_path_d_dx <depth_structure
+  <unwind2_path_d_dx
   >list_append_rcons_sn in H1n; <reverse_append #H1n
   lapply (unwind2_rmap_append_pap_closed f … H1n)
   <reverse_lcons <depth_L_dx #H2n
@@ -53,9 +51,9 @@ theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
   @(subset_eq_trans … (unwind2_term_fsubst …))
   [ @fsubst_eq_repl [ // | // ]
     @(subset_eq_trans … (unwind2_term_iref …))
-    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+    @(subset_eq_canc_sn … (unwind2_term_eq_repl_dx …))
     [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
-    @(subset_eq_trans … (unwind2_lift_term_after …))
+    @(subset_eq_trans … (unwind2_term_after …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
     @nstream_eq_inv_ext #m
@@ -64,8 +62,8 @@ theorem dfr_des_ifr (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
     >list_append_rcons_sn in H1n; <reverse_append #H1n
     lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
     >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
-    lapply (tls_unwind2_rmap_append_closed f … H1n) #H2n
-    <(tr_pap_eq_repl … H2n) -H2n -H1n //
+    lapply (tls_unwind2_rmap_append_closed f … H1n) -H1n #H2n
+    <(tr_pap_eq_repl … H2n) -H2n //
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
index 4e70a6c43212df751914c4ee2321a32997ba6acf..90cd693c3a0777438aee4cc4ea299f1d2cfe7dcb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "delayed_updating/unwind/unwind2_prototerm.ma".
 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_head.ma".
 include "delayed_updating/syntax/path_depth.ma".
@@ -26,7 +26,7 @@ definition ifr (p) (q): relation2 prototerm prototerm ≝
            λt1,t2. ∃n:pnat.
            let r ≝ p●𝗔◗𝗟◗q in
            ∧∧ (𝗟◗q)ᴿ = ↳[n](rᴿ) & r◖𝗱n ϵ t1 &
-              t1[â\8b\94râ\86\90â\86\91[𝐮❨♭(𝗟◗q)❩](t1⋔(p◖𝗦))] ⇔ t2
+              t1[â\8b\94râ\86\90â\96¼[𝐮❨♭(𝗟◗q)❩](t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
index 7634974a54f9a0c6c9dffe13a44d75517c104e51..9bd4cd7c47f21e086d9798e24966f0b02c3c6cbf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
@@ -17,13 +17,12 @@ include "delayed_updating/reduction/ifr.ma".
 include "delayed_updating/unwind/unwind2_constructors.ma".
 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
-include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
+include "delayed_updating/unwind/unwind2_prototerm_inner.ma".
 include "delayed_updating/unwind/unwind2_rmap_head.ma".
 
 include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
 
-include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+include "delayed_updating/syntax/prototerm_proper_inner.ma".
 include "delayed_updating/syntax/path_head_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
 include "delayed_updating/syntax/path_structure_reverse.ma".
@@ -34,16 +33,16 @@ include "delayed_updating/syntax/path_depth_reverse.ma".
 (* Constructions with unwind ************************************************)
 
 theorem ifr_unwind_bi (f) (p) (q) (t1) (t2):
-        t1 ϵ 𝐓 → t1⋔(p◖𝗦) ϵ 𝐏 →
+        t1 ϵ 𝐓 → t1⋔(p◖𝗦) ⧸≬ 𝐈 →
         t1 ➡𝐟[p,q] t2 → ▼[f]t1 ➡𝐟[⊗p,⊗q] ▼[f]t2.
-#f #p #q #t1 #t2 #H1t1 #H2t1 
+#f #p #q #t1 #t2 #H1t1 #H2t1
 * #n * #H1n #Ht1 #Ht2
-@(ex_intro … (↑♭⊗q)) @and3_intro
-[ -H0t1 -Ht1 -Ht2
+@(ex_intro … (↑♭q)) @and3_intro
+[ -H1t1 -H2t1 -Ht1 -Ht2
   >structure_L_sn >structure_reverse
   >H1n >path_head_structure_depth <H1n -H1n //
-| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
-  <unwind2_path_d_dx <depth_structure
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2t1
+  <unwind2_path_d_dx
   >list_append_rcons_sn in H1n; <reverse_append #H1n
   lapply (unwind2_rmap_append_pap_closed f … H1n)
   <reverse_lcons <depth_L_dx #H2n
@@ -52,11 +51,10 @@ theorem ifr_unwind_bi (f) (p) (q) (t1) (t2):
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (unwind2_term_fsubst …))
   [ @fsubst_eq_repl [ // | // ]
-(*  
-    @(subset_eq_trans … (unwind2_term_iref …))
-    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+    @(subset_eq_canc_dx … (unwind2_term_after …))
+    @(subset_eq_canc_sn … (unwind2_term_eq_repl_dx …))
     [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
-    @(subset_eq_trans … (unwind2_lift_term_after …))
+    @(subset_eq_trans … (unwind2_term_after …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
     @nstream_eq_inv_ext #m
@@ -65,13 +63,13 @@ theorem ifr_unwind_bi (f) (p) (q) (t1) (t2):
     >list_append_rcons_sn in H1n; <reverse_append #H1n
     lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
     >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
-    lapply (tls_unwind2_rmap_append_closed f … H1n) #H2n
-    <(tr_pap_eq_repl … H2n) -H2n -H1n //
+    lapply (tls_unwind2_rmap_append_closed f … H1n) -H1n #H2n
+    <(tr_pap_eq_repl … H2n) -H2n //
 (* Note: crux of the proof ends *)
-*)
   | //
   | /2 width=2 by ex_intro/
-  | //
+  | @term_proper_outer #H0 (**) (* full auto does not work *)
+    /3 width=2 by unwind2_term_des_inner/
   ]
 ]
 qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
index b873ed3036aca4daadce71579d2edf86aa8dd5a6..6933e9dbe704b39331ea6d29d503a0254affd711 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -15,8 +15,7 @@
 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".
+include "ground/relocation/tr_id_pap.ma".
 
 (* LIFT FOR PATH ************************************************************)
 
@@ -28,7 +27,7 @@ match p with
 [ list_empty     ⇒ k f (𝐞)
 | list_lcons l q ⇒
   match l with
-  [ label_d n ⇒ lift_gen (A) (λg,p. k g (𝗱(f＠⧣❨n❩)◗p)) (⇂*[n]f) q
+  [ label_d n ⇒ lift_gen (A) (λg,p. k g (𝗱(f＠⧣❨n❩)◗p)) (𝐢) q
   | label_m   ⇒ lift_gen (A) (λg,p. k g (𝗺◗p)) f q
   | label_L   ⇒ lift_gen (A) (λg,p. k g (𝗟◗p)) (⫯f) q
   | label_A   ⇒ lift_gen (A) (λg,p. k g (𝗔◗p)) f q
@@ -61,7 +60,7 @@ lemma lift_empty (A) (k) (f):
 // qed.
 
 lemma lift_d_sn (A) (k) (p) (n) (f):
-      ↑❨(λg,p. k g (𝗱(f＠⧣❨n❩)◗p)), ⇂*[n]f, p❩ = ↑{A}❨k, f, 𝗱n◗p❩.
+      ↑❨(λg,p. k g (𝗱(f＠⧣❨n❩)◗p)), 𝐢, p❩ = ↑{A}❨k, f, 𝗱n◗p❩.
 // qed.
 
 lemma lift_m_sn (A) (k) (p) (f):
@@ -93,7 +92,7 @@ lemma lift_rmap_empty (f):
 // qed.
 
 lemma lift_rmap_d_sn (f) (p) (n):
-      ↑[p](⇂*[ninj n]f) = ↑[𝗱n◗p]f.
+      ↑[p]𝐢 = ↑[𝗱n◗p]f.
 // qed.
 
 lemma lift_rmap_m_sn (f) (p):
@@ -112,12 +111,21 @@ lemma lift_rmap_S_sn (f) (p):
       ↑[p]f = ↑[𝗦◗p]f.
 // qed.
 
+(* Advanced cinstructionswith proj_rmap and tr_id ***************************)
+
+lemma lift_rmap_id (p):
+      (𝐢) = ↑[p]𝐢.
+#p elim p -p //
+* [ #n ] #p #IH //
+qed.
+
 (* Advanced constructions with proj_rmap and path_append ********************)
 
 lemma lift_rmap_append (p2) (p1) (f):
       ↑[p2]↑[p1]f = ↑[p1●p2]f.
 #p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
-[ <lift_rmap_m_sn <lift_rmap_m_sn //
+[ <lift_rmap_d_sn <lift_rmap_d_sn //
+| <lift_rmap_m_sn <lift_rmap_m_sn //
 | <lift_rmap_A_sn <lift_rmap_A_sn //
 | <lift_rmap_S_sn <lift_rmap_S_sn //
 ]
@@ -126,7 +134,7 @@ qed.
 (* Advanced constructions with proj_rmap and path_rcons *********************)
 
 lemma lift_rmap_d_dx (f) (p) (n):
-      ⇂*[ninj n](↑[p]f) = ↑[p◖𝗱n]f.
+      (𝐢) = ↑[p◖𝗱n]f.
 // qed.
 
 lemma lift_rmap_m_dx (f) (p):
@@ -146,5 +154,5 @@ lemma lift_rmap_S_dx (f) (p):
 // qed.
 
 lemma lift_rmap_pap_d_dx (f) (p) (n) (m):
-      ↑[p]f＠⧣❨m+n❩ = ↑[p◖𝗱n]f＠⧣❨m❩+↑[p]f＠⧣❨n❩.
+      m = ↑[p◖𝗱n]f＠⧣❨m❩.
 // qed.

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 1cdcd4650d1b990de616a87dd79a2f8e202b818d..4eeb2ab6d9eda5930dc40cf7fba5e7b0318e4b59 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_prototerm_id.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
 include "delayed_updating/substitution/lift_path_uni.ma".
 include "delayed_updating/syntax/prototerm_constructors.ma".
 
@@ -24,28 +24,24 @@ lemma lift_iref_bi (t1) (t2) (n):
 qed.
 
 lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
-      (𝛗f＠⧣❨n❩.↑[⇂*[n]f]t) ⊆ ↑[f](𝛗n.t).
-#f #t #n #p * #q * #r #Hr #H1 #H2 destruct
-@(ex2_intro … (𝗱n◗𝗺◗r))
+      (𝛗f＠⧣❨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/
 qed-.
 
 lemma lift_iref_dx (f) (t) (n:pnat):
-      ↑[f](𝛗n.t) ⊆ 𝛗f＠⧣❨n❩.↑[⇂*[n]f]t.
+      ↑[f](𝛗n.t) ⊆ 𝛗f＠⧣❨n❩.t.
 #f #t #n #p * #q #Hq #H0 destruct
 elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
-/3 width=1 by in_comp_iref, in_comp_lift_bi/
+/2 width=1 by in_comp_iref/
 qed-.
 
 lemma lift_iref (f) (t) (n:pnat):
-      (𝛗f＠⧣❨n❩.↑[⇂*[n]f]t) ⇔ ↑[f](𝛗n.t).
+      (𝛗f＠⧣❨n❩.t) ⇔ ↑[f](𝛗n.t).
 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/
 qed.
 
 lemma lift_iref_uni (t) (m) (n):
       (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).
-#t #m #n
-@(subset_eq_trans … (lift_iref …))
-<tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni
-/3 width=1 by lift_iref_bi, lift_term_id/
-qed.
+// 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
index 9c4b0f3b5ac350eba4175d9fc10d603361a96d4f..f6759bd1e0fd1f7011adc2bd9116177771628903 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
@@ -15,7 +15,6 @@
 include "delayed_updating/substitution/lift.ma".
 include "ground/relocation/tr_pap_eq.ma".
 include "ground/relocation/tr_pn_eq.ma".
-include "ground/lib/stream_tls_eq.ma".
 
 (* LIFT FOR PATH ************************************************************)
 
@@ -34,7 +33,7 @@ lemma lift_eq_repl (A) (p) (k1) (k2):
 #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 stream_eq_refl/
 | /3 width=1 by/
 | /3 width=1 by tr_push_eq_repl/
 | /3 width=1 by/
@@ -87,7 +86,7 @@ lemma lift_path_lcons (f) (p) (l):
 qed.
 
 lemma lift_path_d_sn (f) (p) (n):
-      (𝗱(f＠⧣❨n❩)◗↑[⇂*[n]f]p) = ↑[f](𝗱n◗p).
+      (𝗱(f＠⧣❨n❩)◗↑[𝐢]p) = ↑[f](𝗱n◗p).
 // qed.
 
 lemma lift_path_m_sn (f) (p):
@@ -106,6 +105,15 @@ lemma lift_path_S_sn (f) (p):
       (𝗦◗↑[f]p) = ↑[f](𝗦◗p).
 // qed.
 
+lemma lift_path_id (p):
+      p = ↑[𝐢]p.
+#p elim p -p //
+* [ #n ] #p #IH //
+[ <lift_path_d_sn //
+| <lift_path_L_sn //
+]
+qed.
+
 lemma lift_path_append (p2) (p1) (f):
       (↑[f]p1)●(↑[↑[p1]f]p2) = ↑[f](p1●p2).
 #p2 #p1 elim p1 -p1 //
@@ -118,29 +126,29 @@ lemma lift_path_append (p2) (p1) (f):
 ]
 qed.
 
-lemma lift_path_d_dx (f) (p) (n):
+lemma lift_path_d_dx (n) (p) (f):
       (↑[f]p)◖𝗱((↑[p]f)＠⧣❨n❩) = ↑[f](p◖𝗱n).
-#f #p #n <lift_path_append //
+#n #p #f <lift_path_append //
 qed.
 
-lemma lift_path_m_dx (f) (p):
+lemma lift_path_m_dx (p) (f):
       (↑[f]p)◖𝗺 = ↑[f](p◖𝗺).
-#f #p <lift_path_append //
+#p #f <lift_path_append //
 qed.
 
-lemma lift_path_L_dx (f) (p):
+lemma lift_path_L_dx (p) (f):
       (↑[f]p)◖𝗟 = ↑[f](p◖𝗟).
-#f #p <lift_path_append //
+#p #f <lift_path_append //
 qed.
 
-lemma lift_path_A_dx (f) (p):
+lemma lift_path_A_dx (p) (f):
       (↑[f]p)◖𝗔 = ↑[f](p◖𝗔).
-#f #p <lift_path_append //
+#p #f <lift_path_append //
 qed.
 
-lemma lift_path_S_dx (f) (p):
+lemma lift_path_S_dx (p) (f):
       (↑[f]p)◖𝗦 = ↑[f](p◖𝗦).
-#f #p <lift_path_append //
+#p #f <lift_path_append //
 qed.
 
 (* COMMENT 
@@ -153,5 +161,4 @@ lemma lift_rmap_tls_d_dx (f) (p) (m) (n):
 <lift_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/substitution/lift_path_after.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
index 869d680fef6a2cec94700f90aef49d9fb4587787..938d2153443f3e300f6279ceb70673eccee8bfee 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_after.ma
@@ -15,7 +15,6 @@
 include "delayed_updating/substitution/lift_eq.ma".
 include "ground/relocation/tr_compose_pap.ma".
 include "ground/relocation/tr_compose_pn.ma".
-include "ground/relocation/tr_compose_tls.ma".
 
 (* LIFT FOR PATH ************************************************************)
 
@@ -23,9 +22,7 @@ include "ground/relocation/tr_compose_tls.ma".
 
 lemma lift_path_after (p) (f1) (f2):
       ↑[f2]↑[f1]p = ↑[f2∘f1]p.
-#p elim p -p [| * ] // [ #n ] #p #IH #f1 #f2
-[ <lift_path_d_sn <lift_path_d_sn <lift_path_d_sn //
-| <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
-  >tr_compose_push_bi //
-]
+#p elim p -p [| * ] // #p #IH #f1 #f2
+<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_path_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_id.ma
deleted file mode 100644 (file)
index 1966c25..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_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 = ↑[𝐢]p.
-#p elim p -p //
-* [ #n ] #p #IH //
-[ <lift_path_d_sn //
-| <lift_path_L_sn //
-]
-qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.ma
new file mode 100644 (file)
index 0000000..f384cf7
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_length.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_eq.ma".
+include "ground/lib/list_length.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+(* Constructions with list_length *******************************************)
+
+lemma lift_path_length (p) (f):
+      ❘p❘ = ❘↑[f]p❘.
+#p elim p -p // * [ #n ] #p #IH #f //
+[ <lift_path_m_sn
+| <lift_path_L_sn
+| <lift_path_A_sn
+| <lift_path_S_sn
+]
+>list_length_lcons >list_length_lcons //
+qed.

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
new file mode 100644 (file)
index 0000000..15d6e09
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_structure.ma
@@ -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/substitution/lift_eq.ma".
+include "delayed_updating/syntax/path_structure.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+(* Constructions with structure *********************************************)
+
+lemma structure_lift_path (p) (f):
+      ⊗p = ⊗↑[f]p.
+#p elim p -p //
+* [ #n ] #p #IH #f //
+[ <lift_path_m_sn <structure_m_sn <structure_m_sn //
+| <lift_path_L_sn <structure_L_sn <structure_L_sn //
+]
+qed.
+
+lemma lift_path_structure (p) (f):
+      ⊗p = ↑[f]⊗p.
+#p elim p -p //
+* [ #n ] #p #IH #f //
+qed.

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 f68010b32a4eabfcd6a6d72f99b42988f3ebe574..9a62cb28a75cbd28645898154147c03729de886e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_uni.ma
@@ -12,9 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_path_id.ma".
+include "delayed_updating/substitution/lift_eq.ma".
 include "ground/relocation/tr_uni_pap.ma".
-include "ground/relocation/tr_uni_tls.ma".
 
 (* LIFT FOR PATH ************************************************************)
 
@@ -22,7 +21,4 @@ include "ground/relocation/tr_uni_tls.ma".
 
 lemma lift_path_d_sn_uni (p) (m) (n):
       (𝗱(n+m)◗p) = ↑[𝐮❨m❩](𝗱(n)◗p).
-#p #m #n
-<lift_path_d_sn <tr_uni_pap >nsucc_pnpred
-<tr_tls_succ_uni //
-qed.
+// 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
index 920a16cf0d2cc59a0c983c6f98cfbbade6406e6f..0b3ba39b001f5f7e1787537fb1cafa0c0ad1c200 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
@@ -38,3 +38,20 @@ lemma lift_term_after (f1) (f2) (t):
 | @subset_equivalence_ext_f1_exteq /2 width=5/
 ]
 qed.
+
+lemma lift_term_id_sn (t):
+      t ⊆ ↑[𝐢]t.
+#t #p #Hp
+>(lift_path_id p)
+/2 width=1 by in_comp_lift_bi/
+qed-.
+
+lemma lift_term_id_dx (t):
+      ↑[𝐢]t ⊆ t.
+#t #p * #q #Hq #H destruct //
+qed-.
+
+lemma lift_term_id (t):
+      t ⇔ ↑[𝐢]t.
+/3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/
+qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
deleted file mode 100644 (file)
index b66b63f..0000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_id.ma
+++ /dev/null
@@ -1,37 +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_path_id.ma".
-
-(* LIFT FOR PROTOTERM *******************************************************)
-
-(* Constructions with tr_id *************************************************)
-
-lemma lift_term_id_sn (t):
-      t ⊆ ↑[𝐢]t.
-#t #p #Hp
->(lift_path_id p)
-/2 width=1 by in_comp_lift_bi/
-qed-.
-
-lemma lift_term_id_dx (t):
-      ↑[𝐢]t ⊆ t.
-#t #p * #q #Hq #H destruct //
-qed-.
-
-lemma lift_term_id (t):
-      t ⇔ ↑[𝐢]t.
-/3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/      
-qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner_proper.ma
new file mode 100644 (file)
index 0000000..042df44
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner_proper.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/syntax/path_inner.ma".
+include "delayed_updating/syntax/path_proper.ma".
+
+(* INNER CONDITION FOR PATH *************************************************)
+
+(* Destructions with proper condition for path ******************************)
+
+lemma path_des_outer_proper (p):
+      p ⧸ϵ 𝐈 → p ϵ 𝐏.
+#p #H1 #H2 destruct
+@H1 -H1 // (**) (* auto fails *)
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma
index 9cab60b87950a5c132f82f4bbf1361a723d5e61c..ff6a53c3932c4a01eac32c3e58993ab8fadb9174 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma
@@ -30,7 +30,12 @@ interpretation
 (* Basic constructions ******************************************************)
 
 lemma ppc_lcons (l) (q): l◗q ϵ 𝐏.
-#l #p #H destruct
+#l #q #H0 destruct
+qed.
+
+lemma ppc_rcons (l) (q): q◖l ϵ 𝐏.
+#l #q #H
+elim (eq_inv_list_empty_rcons ??? H)
 qed.
 
 (* Basic inversions ********************************************************)

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper.ma
index b2bb92cf83b41f12cc543472df230c20ce3b2c5b..31fa1ca4a04dfe5eb077b2606fd0c5a0c22450d8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper.ma
@@ -30,13 +30,16 @@ lemma tpc_i (t):
 #H elim (Ht H)
 qed.
 
-(* Basic inversions *********************************************************)
+(* Basic destructions *******************************************************)
 
-lemma in_ppc_comp_trans (t) (p):
+lemma in_comp_tpc_trans (t) (p):
       p ϵ t → t ϵ 𝐏 → p ϵ 𝐏.
 #t #p #Hp #Ht
 @(Ht … Hp)
 qed-.
 
-lemma tpc_e (t): 𝐞 ϵ t → t ϵ 𝐏 → ⊥.
-/2 width=5 by in_ppc_comp_trans/ qed-.
+(* Basic inversions *********************************************************)
+
+lemma tpc_inv_empty (t):
+      (𝐞) ϵ t → t ϵ 𝐏 → ⊥.
+/2 width=5 by in_comp_tpc_trans/ qed-.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper_inner.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper_inner.ma
new file mode 100644 (file)
index 0000000..e366547
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper_inner.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/syntax/prototerm_proper.ma".
+include "delayed_updating/syntax/path_inner_proper.ma".
+include "ground/lib/subset_overlap.ma".
+
+(* PROPER CONDITION FOR PROTOTERM *******************************************)
+
+(* Constructions with inner condition for prototerm *************************)
+
+lemma term_proper_outer (t):
+      t ⧸≬ 𝐈 → t ϵ 𝐏.
+/4 width=3 by path_des_outer_proper, subset_ol_i/
+qed.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_inner.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_inner.ma
new file mode 100644 (file)
index 0000000..2ec01a2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_path_inner.ma
@@ -0,0 +1,28 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/unwind/unwind2_path_structure.ma".
+include "delayed_updating/syntax/path_inner.ma".
+
+(* UNWIND FOR PATH **********************************************************)
+
+(* Destructions with inner condition for path *******************************)
+
+lemma unwind2_path_des_inner (f) (p):
+      ▼[f]p ϵ 𝐈 → p ϵ 𝐈.
+#f #p @(list_ind_rcons … p) -p //
+#p * [ #n ] #_ //
+<unwind2_path_d_dx #H0
+elim (pic_inv_d_dx … H0)
+qed-.

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma
index 4245a6638b97c90622400739efa489c29d1f0dad..522ad9455a99868fc3eb73668cbf597a6f89e857 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_preterm_fsubst.ma
@@ -27,7 +27,7 @@ lemma unwind2_term_fsubst_sn (f) (t) (u) (p): u ϵ 𝐏 →
 #f #t #u #p #Hu #ql * *
 [ #rl * #r #Hr #H1 #H2 destruct
   >unwind2_path_append_proper_dx
-  /4 width=5 by in_comp_unwind2_path_term, in_ppc_comp_trans, or_introl, ex2_intro/
+  /4 width=5 by in_comp_unwind2_path_term, in_comp_tpc_trans, or_introl, ex2_intro/
 | * #q #Hq #H1 #H0
   @(ex2_intro … H1) @or_intror @conj // *
   [ <list_append_empty_dx #H2 destruct
@@ -43,7 +43,7 @@ lemma unwind2_term_fsubst_dx (f) (t) (u) (p): u ϵ 𝐏 → p ϵ ▵t → t ϵ 
 #f #t #u #p #Hu #H1p #H2p #ql * #q * *
 [ #r #Hu #H1 #H2 destruct
   @or_introl @ex2_intro
-  [|| <unwind2_path_append_proper_dx /2 width=5 by in_ppc_comp_trans/ ]
+  [|| <unwind2_path_append_proper_dx /2 width=5 by in_comp_tpc_trans/ ]
   /2 width=3 by ex2_intro/
 | #Hq #H0 #H1 destruct
   @or_intror @conj [ /2 width=1 by in_comp_unwind2_path_term/ ] *

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_inner.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_inner.ma
new file mode 100644 (file)
index 0000000..7cbe69e
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_inner.ma
@@ -0,0 +1,28 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/unwind/unwind2_prototerm.ma".
+include "delayed_updating/unwind/unwind2_path_inner.ma".
+include "ground/lib/subset_overlap.ma".
+
+(* UNWIND FOR PROTOTERM *****************************************************)
+
+(* Destructions with inner condition for path *******************************)
+
+lemma unwind2_term_des_inner (f) (t):
+      ▼[f]t ≬ 𝐈 → t ≬ 𝐈.
+#f #t * #p * #q #Hq #H0 #Hp destruct
+@(subset_ol_i … Hq) -Hq (**) (* auto does not work *)
+@(unwind2_path_des_inner … Hp)
+qed-.