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".
interpretation
"inner variable reference by depth (prototerm)"
- 'Phi n t = (prototerm_node_1_2 (label_d n) label_m t).
+ 'Tau n t = (prototerm_node_1_2 (label_d n) label_m t).
interpretation
"name-free functional abstraction (prototerm)"
(* Basic constructions *******************************************************)
lemma in_comp_iref (t) (q) (n):
- q ϵ t â\86\92 ð\9d\97±nâ\97\97ð\9d\97ºâ\97\97q ϵ ð\9d\9b\97n.t.
+ q ϵ t â\86\92 ð\9d\97±nâ\97\97ð\9d\97ºâ\97\97q ϵ ð\9d\9b\95n.t.
/2 width=3 by ex2_intro/ qed.
-(* Basic Inversions *********************************************************)
+(* Basic inversions *********************************************************)
lemma in_comp_inv_iref (t) (p) (n):
- p ϵ ð\9d\9b\97n.t →
+ p ϵ ð\9d\9b\95n.t →
∃∃q. 𝗱n◗𝗺◗q = p & q ϵ t.
#t #p #n * #q #Hq #Hp
/2 width=3 by ex2_intro/
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