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 "delayed_updating/relocation/tr_minus_pn.ma".
16 include "ground/relocation/tr_pap_pn.ma".
17 include "ground/relocation/tr_pap_lt.ma".
18 include "ground/arith/nat_rplus_succ.ma".
19 include "ground/arith/pnat_le.ma".
21 (* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
23 (* Constructions with tr_pap ************************************************)
25 lemma tr_pap_minus_le (n) (p) (f):
28 #n @(nat_ind_succ … n) -n [| #n #IHn ]
30 lapply (tr_pap_increasing f p) #H2f
31 >(ple_antisym … H2f H1f) in ⊢ (??%?); -H1f -H2f //
32 | #p elim p -p [| #p #IHp ]
33 #f elim (tr_map_split f) * #g #H0 destruct
36 <tr_pap_next <nrplus_succ_dx #Hf
37 lapply (ple_inv_succ_bi … Hf) -Hf #Hf
38 <tr_minus_next_succ /2 width=1 by/
39 | <tr_minus_push_succ <tr_pap_push <tr_pap_push <nrplus_succ_sn #Hf
40 lapply (ple_inv_succ_bi … Hf) -Hf #Hf