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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/notation/relations/predicate_t_1.ma".
16 include "ground/relocation/gr_pat.ma".
18 (* TOTALITY CONDITION FOR GENERIC RELOCATION MAPS ***************************)
21 definition gr_ist: predicate gr_map ≝
22 λf. ∀i. ∃j. @❪i,f❫ ≘ j.
25 "totality condition (generic relocation maps)"
26 'PredicateT f = (gr_ist f).
28 (* Basic inversions *********************************************************)
30 (*** istot_inv_push *)
31 lemma gr_ist_inv_push (g): 𝐓❪g❫ → ∀f. ⫯f = g → 𝐓❪f❫.
32 #g #Hg #f #H #i elim (Hg (↑i)) -Hg
33 #j #Hg elim (gr_pat_inv_succ_push … Hg … H) -Hg -H /2 width=3 by ex_intro/
36 (*** istot_inv_next *)
37 lemma gr_ist_inv_next (g): 𝐓❪g❫ → ∀f. ↑f = g → 𝐓❪f❫.
38 #g #Hg #f #H #i elim (Hg i) -Hg
39 #j #Hg elim (gr_pat_inv_next … Hg … H) -Hg -H /2 width=2 by ex_intro/
42 (* Constructions with gr_tl *************************************************)
45 lemma gr_ist_tl (f): 𝐓❪f❫ → 𝐓❪⫰f❫.
46 #f cases (gr_map_split_tl f) *
47 /2 width=3 by gr_ist_inv_next, gr_ist_inv_push/