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/gr_tl_eq.ma".
16 include "ground/relocation/gr_id.ma".
18 (* IDENTITY ELEMENT FOR GENERIC RELOCATION MAPS ******************************************************)
20 (* Properties with gr_eq *)
22 corec lemma gr_id_eq (f): ⫯f ≡ f → 𝐢 ≡ f.
23 cases gr_id_unfold #Hf
24 cases (gr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
26 @gr_eq_push [3:|*: // ]
27 /3 width=5 by gr_eq_inv_push_bi/
30 (* Inversions with gr_eq *)
32 (* Note: this has the same proof of the previous *)
33 corec lemma gr_id_inv_eq (f): 𝐢 ≡ f → ⫯f ≡ f.
34 cases gr_id_unfold #Hf
35 cases (gr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
37 @gr_eq_push [3:|*: // ]
38 /3 width=5 by gr_eq_inv_push_bi/