update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / prototerm_constructors.ma

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 fd86ef975a39b862aaf05ac99dc5efd298fb10ed..5bb66e16ab112f1ab94db7db70cba521bc150131 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
@@ -15,7 +15,7 @@
 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/lamda_1.ma".
 include "delayed_updating/notation/functions/at_2.ma".
 
@@ -41,11 +41,11 @@ 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
   "name-free functional abstraction (prototerm)"
@@ -55,8 +55,22 @@ 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.
+
+(* 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-.
+
+(* COMMENT
 lemma prototerm_in_root_inv_lcons_oref:
       ∀p,l,n. l◗p ϵ ▵#n →
       ∧∧ 𝗱n = l & 𝐞 = p.
@@ -67,7 +81,7 @@ elim (eq_inv_list_empty_append … e0) -e0 #H0 #_
 qed-.
 
 lemma prototerm_in_root_inv_lcons_iref:
-      â\88\80t,p,l,n. lâ\97\97p ϵ â\96µð\9d\9b\97n.t →
+      â\88\80t,p,l,n. lâ\97\97p ϵ â\96µð\9d\9b\95n.t →
       ∧∧ 𝗱n = l & p ϵ ▵ɱ.t.
 #t #p #l #n * #q * #r #Hr
 <list_append_lcons_sn #H0 destruct -H0
@@ -98,3 +112,4 @@ 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-.
+*)