partial 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 5bb66e16ab112f1ab94db7db70cba521bc150131..8bffdb64ae0555df03894b6793f712f21b92e81a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
@@ -16,6 +16,7 @@ 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/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".
 
@@ -47,6 +48,10 @@ interpretation
   "inner variable reference by depth (prototerm)"
   '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)"
   'Lamda t = (prototerm_node_1 label_L t).
@@ -61,6 +66,10 @@ 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):
@@ -70,6 +79,13 @@ lemma in_comp_inv_iref (t) (p) (k):
 /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 →