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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "ground/relocation/fr2_nat.ma".
16
17 (* NON-NEGATIVE APPLICATION FOR FINITE RELOCATION MAPS WITH PAIRS ***********)
18
19 (* Main constructions *******************************************************)
20
21 (*** at_mono *)
22 theorem fr2_nat_mono (f) (l):
23         ∀l1. @❨l, f❩ ≘ l1 → ∀l2. @❨l, f❩ ≘ l2 → l1 = l2.
24 #f #l #l1 #H elim H -f -l -l1
25 [ #l #x #H <(fr2_nat_inv_empty … H) -x //
26 | #f #d #h #l #l1 #Hld #_ #IH #x #H
27   lapply (fr2_nat_inv_lcons_lt … H Hld) -H -Hld /2 width=1 by/
28 | #f #d #h #l #l1 #Hdl #_ #IH #x #H
29   lapply (fr2_nat_inv_lcons_ge … H Hdl) -H -Hdl /2 width=1 by/
30 ]
31 qed-.