1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "delayed_updating/syntax/preterm.ma".
16 include "delayed_updating/notation/functions/hash_1.ma".
17 include "delayed_updating/notation/functions/phi_2.ma".
18 include "delayed_updating/notation/functions/lamda_1.ma".
19 include "delayed_updating/notation/functions/at_2.ma".
21 (* CONSTRUCTORS FOR PRETERM *************************************************)
23 definition preterm_node_0 (l): preterm ≝
26 definition preterm_node_1 (l): preterm → preterm ≝
27 λt,p. ∃∃q. q ϵ⬦ t & l;q = p.
29 definition preterm_node_2 (l1) (l2): preterm → preterm → preterm ≝
31 ∨∨ ∃∃q. q ϵ⬦ t1 & l1;q = p
32 | ∃∃q. q ϵ⬦ t2 & l2;q = p.
35 "outer variable reference by depth (preterm)"
36 'Hash n = (preterm_node_0 (label_node_d n)).
39 "inner variable reference by depth (preterm)"
40 'Phi n t = (preterm_node_1 (label_node_d n) t).
43 "name-free functional abstraction (preterm)"
44 'Lamda t = (preterm_node_1 label_edge_L t).
47 "application (preterm)"
48 'At u t = (preterm_node_2 label_edge_S label_edge_A u t).
50 (* Basic Inversions *********************************************************)
52 lemma preterm_in_root_inv_lcons_oref:
56 <list_append_lcons_sn #H0 destruct -H0
57 elim (eq_inv_list_empty_append … e0) -e0 #H0 #_
61 lemma preterm_in_root_inv_lcons_iref:
62 ∀t,p,l,n. l;p ϵ▵ 𝛗n.t →
65 <list_append_lcons_sn * #r #Hr #H0 destruct
66 /3 width=2 by ex_intro, conj/
69 lemma preterm_in_root_inv_lcons_abst:
73 <list_append_lcons_sn * #r #Hr #H0 destruct
74 /3 width=2 by ex_intro, conj/
77 lemma preterm_in_root_inv_lcons_appl:
78 ∀u,t,p,l. l;p ϵ▵ @u.t →
82 <list_append_lcons_sn * * #r #Hr #H0 destruct
83 /4 width=2 by ex_intro, or_introl, or_intror, conj/