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".
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)"
- 'Tau 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)"
(* Basic constructions *******************************************************)
-lemma in_comp_iref (t) (q) (n):
- q Ļµ t ā š±nāšŗāq Ļµ šn.t.
+lemma in_comp_iref (t) (q) (k):
+ q Ļµ t ā š±kāšŗāq Ļµ šk.t.
+/2 width=3 by ex2_intro/ qed.
+
+lemma in_comp_iref2 (t) (q) (k) (d):
+ q Ļµ t ā š±āØk,dā©āšŗāq Ļµ šāØk,dā©.t.
/2 width=3 by ex2_intro/ qed.
(* Basic inversions *********************************************************)
-lemma in_comp_inv_iref (t) (p) (n):
- p Ļµ šn.t ā
- āāq. š±nāšŗāq = p & q Ļµ t.
-#t #p #n * #q #Hq #Hp
+lemma in_comp_inv_iref (t) (p) (k):
+ p Ļµ šk.t ā
+ āāq. š±kāšŗāq = p & q Ļµ t.
+#t #p #k * #q #Hq #Hp
/2 width=3 by ex2_intro/
qed-.
+
+lemma in_comp_inv_iref2 (t) (p) (k) (d):
+ p Ļµ šāØk,dā©.t ā
+ āāq. š±āØk,dā©āšŗāq = p & q Ļµ t.
+#t #p #k #d * #q #Hq #Hp
+/2 width=3 by ex2_intro/
+qed-.
+
(* COMMENT
lemma prototerm_in_root_inv_lcons_oref:
āp,l,n. lāp Ļµ āµ#n ā