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/notation/relations/predicate_u_1.ma".
16 include "ground/relocation/gr_isi.ma".
18 (* UNIFORMITY CONDITION FOR GENERIC RELOCATION MAPS *************************)
21 inductive gr_isu: predicate gr_map ā
23 | gr_isu_isi (f): šāŖfā« ā gr_isu f
25 | gr_isu_next (f): gr_isu f ā āg. āf = g ā gr_isu g
29 "uniformity condition (generic relocation maps)"
30 'PredicateU f = (gr_isu f).
32 (* Basic inversions *********************************************************)
34 (*** isuni_inv_push *)
35 lemma gr_isu_inv_push (g): šāŖgā« ā āf. ā«Æf = g ā šāŖfā«.
37 [ /2 width=3 by gr_isi_inv_push/
38 | #f #_ #g #H #x #Hx destruct
39 elim (eq_inv_gr_push_next ā¦ Hx)
43 (*** isuni_inv_next *)
44 lemma gr_isu_inv_next (g): šāŖgā« ā āf. āf = g ā šāŖfā«.
46 [ #x #Hx elim (gr_isi_inv_next ā¦ Hf ā¦ Hx)
47 | #g #H #x #Hx destruct
48 >(eq_inv_gr_next_bi ā¦ Hx) -x //
52 (* Basic destructions *******************************************************)
54 (*** isuni_fwd_push *)
55 lemma gr_isu_fwd_push (g): šāŖgā« ā āf. ā«Æf = g ā šāŖfā«.
56 /3 width=3 by gr_isu_inv_push, gr_isu_isi/ qed-.