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 include "ground/relocation/pr_tl_eq.ma".
16 include "ground/relocation/pr_id.ma".
18 (* IDENTITY ELEMENT FOR PARTIAL RELOCATION MAPS *****************************)
20 (* Constructions with pr_eq *************************************************)
22 corec lemma pr_id_eq (f): ⫯f ≐ f → 𝐢 ≐ f.
23 cases pr_id_unfold #Hf
24 cases (pr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
26 @pr_eq_push [3:|*: // ]
27 /3 width=5 by pr_eq_inv_push_bi/
30 (* Inversions with pr_eq ****************************************************)
32 (* Note: this has the same proof of the previous *)
33 corec lemma pr_id_inv_eq (f): 𝐢 ≐ f → ⫯f ≐ f.
34 cases pr_id_unfold #Hf
35 cases (pr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
37 @pr_eq_push [3:|*: // ]
38 /3 width=5 by pr_eq_inv_push_bi/