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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 "basic_2/unfold/gr2.ma".
16
17 (* GENERIC RELOCATION WITH PAIRS ********************************************)
18
19 (* Main properties **********************************************************)
20
21 theorem at_mono: ∀des,i,i1. @[i] des ≡ i1 → ∀i2. @[i] des ≡ i2 → i1 = i2.
22 #des #i #i1 #H elim H -des -i -i1
23 [ #i #x #H <(at_inv_nil … H) -x //
24 | #des #d #e #i #i1 #Hid #_ #IHi1 #x #H
25   lapply (at_inv_cons_lt … H Hid) -H -Hid /2 width=1/
26 | #des #d #e #i #i1 #Hdi #_ #IHi1 #x #H
27   lapply (at_inv_cons_ge … H Hdi) -H -Hdi /2 width=1/
28 ]
29 qed-.