X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsubstitution%2Flift_eq.ma;h=fad4995de2f7f7af8fa789a1cfb7308d4c8a7396;hb=dfcad1c1a698bac1b7fb6a5f59393b28f45182af;hp=ae3ffbdc6fbdef2165f3b937411c2d429e0c96ef;hpb=8db3579bec4d9a97af526f95a179587a2fbfe3e3;p=helm.git

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 ae3ffbdc6..fad4995de 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_eq.ma
@@ -13,12 +13,19 @@
 (**************************************************************************)
 
 include "delayed_updating/substitution/lift.ma".
-include "ground/notation/relations/ringeq_3.ma".
+(*
+include "ground/relocation/tr_uni_compose.ma".
+include "ground/relocation/tr_compose_compose.ma".
+include "ground/relocation/tr_compose_eq.ma".
+*)
+include "ground/relocation/tr_pap_eq.ma".
+include "ground/relocation/tr_pn_eq.ma".
+include "ground/lib/stream_tls_eq.ma".
 
 (* LIFT FOR PATH ***********************************************************)
 
 definition lift_exteq (A): relation2 (lift_continuation A) (lift_continuation A) ≝
-           λk1,k2. ∀p,f. k1 p f = k2 p f.
+           λk1,k2. ∀f1,f2,p. f1 ≗ f2 → k1 f1 p = k2 f2 p.
 
 interpretation
   "extensional equivalence (lift continuation)"
@@ -26,58 +33,91 @@ interpretation
 
 (* Constructions with lift_exteq ********************************************)
 
-lemma lift_eq_repl_sn (A) (p) (k1) (k2) (f):
-      k1 ≗{A} k2 → ↑❨k1, p, f❩ = ↑❨k2, p, f❩.
-#A #p @(path_ind_lift … p) -p [| #n | #n #l0 #q ]
-[ #k1 #k2 #f #Hk <lift_empty <lift_empty //
-|*: #IH #k1 #k2 #f #Hk /2 width=1 by/
+lemma lift_eq_repl (A) (p) (k1) (k2):
+      k1 ≗{A} k2 → stream_eq_repl … (λf1,f2. ↑❨k1, f1, p❩ = ↑❨k2, f2, p❩).
+#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):
-      ↑❨λp2.k(l◗p2),p,f❩ = ↑{A}❨λp2.k((l◗𝐞)●p2),p,f❩.
-#A #k #f #p #l
-@lift_eq_repl_sn #p2 #g // (**) (* auto fails with typechecker failure *)
+lemma lift_lcons_alt (A) (k) (f) (p) (l): k ≗ k →
+      ↑❨λg,p2. k g (l◗p2), f, p❩ = ↑{A}❨λg,p2. k g ((l◗𝐞)●p2), f, p❩.
+#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):
-      ↑❨λp2.k(p1●l◗p2),p,f❩ = ↑{A}❨λp2.k(p1◖l●p2),p,f❩.
-#A #k #f #p1 #p #l
-@lift_eq_repl_sn #p2 #g
-<list_append_rcons_sn //
+lemma lift_append_rcons_sn (A) (k) (f) (p1) (p) (l): k ≗ k →
+      ↑❨λg,p2. k g (p1●l◗p2), f, p❩ = ↑{A}❨λg,p2. k g (p1◖l●p2), f, p❩.
+#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 ≗ proj_path.
+// qed.
+
+lemma lift_path_eq_repl (p):
+      stream_eq_repl … (λf1,f2. ↑[f1]p = ↑[f2]p).
+/2 width=1 by lift_eq_repl/ qed.
+
 lemma lift_path_append_sn (p) (f) (q):
-      q●↑[f]p = ↑❨(λp. proj_path (q●p)), p, f❩.
-#p @(path_ind_lift … p) -p // [ #n #l #p |*: #p ] #IH #f #q
-[ <lift_d_lcons_sn <lift_d_lcons_sn <IH -IH //
-| <lift_L_sn <lift_L_sn >lift_lcons_alt >lift_append_rcons_sn
-  <IH <IH -IH <list_append_rcons_sn //
-| <lift_A_sn <lift_A_sn >lift_lcons_alt >lift_append_rcons_sn
-  <IH <IH -IH <list_append_rcons_sn //
-| <lift_S_sn <lift_S_sn >lift_lcons_alt >lift_append_rcons_sn
-  <IH <IH -IH <list_append_rcons_sn //
-]
+      q●↑[f]p = ↑❨(λg,p. proj_path g (q●p)), f, p❩.
+#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):
-      l◗↑[f]p = ↑❨(λp. proj_path (l◗p)), p, f❩.
+      l◗↑[f]p = ↑❨(λg,p. proj_path g (l◗p)), f, p❩.
 #f #p #l
 >lift_lcons_alt <lift_path_append_sn //
 qed.
 
+lemma lift_path_d_sn (f) (p) (n):
+      (𝗱(f@❨n❩)◗↑[⇂*[n]f]p) = ↑[f](𝗱n◗p).
+// qed.
+
+lemma lift_path_m_sn (f) (p):
+      (𝗺◗↑[f]p) = ↑[f](𝗺◗p).
+// qed.
+
 lemma lift_path_L_sn (f) (p):
-      𝗟◗↑[⫯f]p = ↑[f](𝗟◗p).
+      (𝗟◗↑[⫯f]p) = ↑[f](𝗟◗p).
 // qed.
 
 lemma lift_path_A_sn (f) (p):
-      𝗔◗↑[f]p = ↑[f](𝗔◗p).
+      (𝗔◗↑[f]p) = ↑[f](𝗔◗p).
 // qed.
 
 lemma lift_path_S_sn (f) (p):
-      𝗦◗↑[f]p = ↑[f](𝗦◗p).
+      (𝗦◗↑[f]p) = ↑[f](𝗦◗p).
 // qed.
+(* COMMENT 
+
+(* Advanced constructions with proj_rmap and stream_tls *********************)
+
+lemma lift_rmap_tls_d_dx (f) (p) (m) (n):
+      ⇂*[m+n]↑[p]f ≗ ⇂*[m]↑[p◖𝗱n]f.
+#f #p #m #n
+<lift_rmap_d_dx >nrplus_inj_dx
+/2 width=1 by tr_tls_compose_uni_dx/
+qed.
+*)