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_isi_id.ma".
16 include "ground/relocation/gr_coafter_coafter.ma".
18 (* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ********************)
20 (* Constructions with gr_isi ************************************************)
22 (*** coafter_isid_sn *)
23 corec lemma gr_coafter_isi_sn:
24 âf1. đâŞf1⍠â âf2. f1 ~â f2 â f2.
25 #f1 * -f1 #f1 #g1 #Hf1 #H1 #f2
26 cases (gr_map_split_tl f2) #H2
27 /3 width=7 by gr_coafter_push, gr_coafter_refl/
30 (*** coafter_isid_dx *)
31 corec lemma gr_coafter_isi_dx:
32 âf2,f. đâŞf2⍠â đâŞf⍠â âf1. f1 ~â f2 â f.
33 #f2 #f * -f2 #f2 #g2 #Hf2 #H2 * -f #f #g #Hf #H #f1
34 cases (gr_map_split_tl f1) #H1
35 [ /3 width=7 by gr_coafter_refl/
36 | @(gr_coafter_next ⌠H1 ⌠H) /3 width=3 by gr_isi_push/
40 (* Inversions with gr_isi ***************************************************)
42 (*** coafter_isid_inv_sn *)
43 lemma gr_coafter_isi_inv_sn:
44 âf1,f2,f. f1 ~â f2 â f â đâŞf1⍠â f2 ⥠f.
45 /3 width=6 by gr_coafter_isi_sn, gr_coafter_mono/ qed-.
47 (*** coafter_isid_inv_dx *)
48 lemma gr_coafter_isi_inv_dx:
49 âf1,f2,f. f1 ~â f2 â f â đâŞf2⍠â đâŞfâŤ.
50 /4 width=4 by gr_eq_id_isi, gr_coafter_isi_dx, gr_coafter_mono/ qed-.