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 *)
13 (**************************************************************************)
15 (**) (* reverse include *)
16 include "ground/lib/subset_ext_equivalence.ma".
17 include "delayed_updating/substitution/lift_path_eq.ma".
18 include "delayed_updating/substitution/lift_prototerm.ma".
20 (* LIFT FOR PROTOTERM *******************************************************)
22 (* Constructions with subset_equivalence ************************************)
24 lemma lift_term_eq_repl_sn (f1) (f2) (t):
25 f1 ≗ f2 → 🠡[f1]t ⇔ 🠡[f2]t.
26 /3 width=1 by subset_equivalence_ext_f1_exteq, lift_path_eq_repl/
29 lemma lift_term_eq_repl_dx (f) (t1) (t2):
30 t1 ⇔ t2 → 🠡[f]t1 ⇔ 🠡[f]t2.
31 /2 width=1 by subset_equivalence_ext_f1_bi/
34 lemma lift_term_grafted_sn (f) (t) (p):
35 🠡[🠢[f]p](t⋔p) ⊆ (🠡[f]t)⋔(🠡[f]p).
36 #f #t #p #q * #r #Hr #H0 destruct
37 /2 width=3 by ex2_intro/
40 lemma lift_term_grafted_dx (f) (t) (p):
41 (🠡[f]t)⋔(🠡[f]p) ⊆ 🠡[🠢[f]p](t⋔p).
42 #f #t #p #q * #r #Hr #H0
43 elim (lift_path_inv_append_sn … (sym_eq … H0)) -H0
44 #p0 #q0 #Hp0 #Hq0 #H0 destruct
45 lapply (lift_path_inj … Hp0) -Hp0 #Hp0 destruct
46 /2 width=1 by in_comp_lift_path_term/
49 lemma lift_term_grafted (f) (t) (p):
50 🠡[🠢[f]p](t⋔p) ⇔ (🠡[f]t)⋔(🠡[f]p).
51 /3 width=1 by lift_term_grafted_sn, lift_term_grafted_dx, conj/ qed.
53 lemma lift_term_grafted_S (f) (t) (p):
54 🠡[🠢[f]p](t⋔(p◖𝗦)) ⇔ (🠡[f]t)⋔((🠡[f]p)◖𝗦).