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 "ground/relocation/pr_tl_eq_eq.ma".
16 include "ground/relocation/pr_isi.ma".
18 (* IDENTITY CONDITION FOR PARTIAL RELOCATION MAPS ***************************)
20 (* Constructions with pr_eq *************************************************)
22 (*** isid_eq_repl_back *)
23 corec lemma pr_isi_eq_repl_back:
24 pr_eq_repl_back … pr_isi.
26 cases (pr_isi_inv_gen … H) -H #g1 #Hg1 #H1 #f2 #Hf
27 cases (pr_eq_inv_push_sn … Hf … H1) -f1
28 /3 width=3 by pr_isi_push/
31 (*** isid_eq_repl_fwd *)
32 lemma pr_isi_eq_repl_fwd:
33 pr_eq_repl_fwd … pr_isi.
34 /3 width=3 by pr_isi_eq_repl_back, pr_eq_repl_sym/ qed-.
36 (* Main inversions with pr_eq ***********************************************)
38 (*** isid_inv_eq_repl *)
39 corec theorem pr_isi_inv_eq_repl (g1) (g2): 𝐈❨g1❩ → 𝐈❨g2❩ → g1 ≡ g2.
41 cases (pr_isi_inv_gen … H1) -H1
42 cases (pr_isi_inv_gen … H2) -H2
43 /3 width=5 by pr_eq_push/
46 (* Alternative definition with pr_eq ****************************************)
49 corec lemma pr_eq_push_isi (f): ⫯f ≡ f → 𝐈❨f❩.
50 #H cases (pr_eq_inv_push_sn … H) -H
51 /4 width=3 by pr_isi_push, pr_eq_trans/
54 (*** eq_push_inv_isid *)
55 corec lemma pr_isi_inv_eq_push (g): 𝐈❨g❩ → ⫯g ≡ g.
57 /3 width=5 by pr_eq_push/