X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsyntax%2Fprototerm_constructors.ma;h=8bffdb64ae0555df03894b6793f712f21b92e81a;hb=797a607af83f82102033270087722a7e59ddcd17;hp=fd86ef975a39b862aaf05ac99dc5efd298fb10ed;hpb=13584a37bbcde10e03c8a488f5b93e1e042da0a6;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
index fd86ef975..8bffdb64a 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
@@ -15,7 +15,8 @@
 include "delayed_updating/syntax/prototerm.ma".
 include "delayed_updating/notation/functions/m_hook_1.ma".
 include "delayed_updating/notation/functions/hash_1.ma".
-include "delayed_updating/notation/functions/phi_2.ma".
+include "delayed_updating/notation/functions/tau_2.ma".
+include "delayed_updating/notation/functions/tau_3.ma".
 include "delayed_updating/notation/functions/lamda_1.ma".
 include "delayed_updating/notation/functions/at_2.ma".
 
@@ -41,11 +42,15 @@ interpretation
 
 interpretation
   "outer variable reference by depth (prototerm)"
-  'Hash n = (prototerm_node_0 (label_d n)).
+  'Hash k = (prototerm_node_0 (label_d k)).
 
 interpretation
   "inner variable reference by depth (prototerm)"
-  'Phi n t = (prototerm_node_1_2 (label_d n) label_m t).
+  'Tau k t = (prototerm_node_1_2 (label_d k) label_m t).
+
+interpretation
+  "inner variable reference by depth with offset (prototerm)"
+  'Tau k d t = (prototerm_node_1_2 (label_d2 k d) label_m t).
 
 interpretation
   "name-free functional abstraction (prototerm)"
@@ -55,8 +60,33 @@ interpretation
   "application (prototerm)"
   'At u t = (prototerm_node_2 label_S label_A u t).
 
-(* Basic Inversions *********************************************************)
+(* Basic constructions *******************************************************)
+
+lemma in_comp_iref (t) (q) (k):
+      q ϵ t → 𝗱k◗𝗺◗q ϵ 𝛕k.t.
+/2 width=3 by ex2_intro/ qed.
+
+lemma in_comp_iref2 (t) (q) (k) (d):
+      q ϵ t → 𝗱❨k,d❩◗𝗺◗q ϵ 𝛕❨k,d❩.t.
+/2 width=3 by ex2_intro/ qed.
+
+(* Basic inversions *********************************************************)
+
+lemma in_comp_inv_iref (t) (p) (k):
+      p ϵ 𝛕k.t →
+      ∃∃q. 𝗱k◗𝗺◗q = p & q ϵ t.
+#t #p #k * #q #Hq #Hp
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma in_comp_inv_iref2 (t) (p) (k) (d):
+      p ϵ 𝛕❨k,d❩.t →
+      ∃∃q. 𝗱❨k,d❩◗𝗺◗q = p & q ϵ t.
+#t #p #k #d * #q #Hq #Hp
+/2 width=3 by ex2_intro/
+qed-.
 
+(* COMMENT
 lemma prototerm_in_root_inv_lcons_oref:
       ∀p,l,n. l◗p ϵ ▵#n →
       ∧∧ 𝗱n = l & 𝐞 = p.
@@ -67,7 +97,7 @@ elim (eq_inv_list_empty_append … e0) -e0 #H0 #_
 qed-.
 
 lemma prototerm_in_root_inv_lcons_iref:
-      ∀t,p,l,n. l◗p ϵ ▵𝛗n.t →
+      ∀t,p,l,n. l◗p ϵ ▵𝛕n.t →
       ∧∧ 𝗱n = l & p ϵ ▵ɱ.t.
 #t #p #l #n * #q * #r #Hr
 <list_append_lcons_sn #H0 destruct -H0
@@ -98,3 +128,4 @@ lemma prototerm_in_root_inv_lcons_appl:
 <list_append_lcons_sn #H0 destruct
 /4 width=2 by ex_intro, or_introl, or_intror, conj/
 qed-.
+*)