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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
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9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
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14
15 include "ground/relocation/pr_pat_id.ma".
16 include "ground/relocation/pr_pat_pat.ma".
17
18 (* POSITIVE APPLICATION FOR PARTIAL RELOCATION MAPS *************************)
19
20 (* Advanced destructions with pr_id *****************************************)
21
22 (*** at_id_fwd *)
23 lemma pr_pat_id_des (i1) (i2):
24       @❚i1,𝐢❩ â‰˜ i2 â†’ i1 = i2.
25 /2 width=4 by pr_pat_mono/ qed-.
26
27 (* Main constructions with pr_id ********************************************)
28
29 (*** at_div_id_dx *)
30 theorem pr_pat_div_id_dx (f):
31         H_pr_pat_div f ð¢ ð¢ f.
32 #f #jf #j0 #j #Hf #H0
33 lapply (pr_pat_id_des â€Š H0) -H0 #H destruct
34 /2 width=3 by ex2_intro/
35 qed-.
36
37 (*** at_div_id_sn *)
38 theorem pr_pat_div_id_sn (f):
39         H_pr_pat_div ð¢ f f ð¢.
40 /3 width=6 by pr_pat_div_id_dx, pr_pat_div_comm/ qed-.