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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/relocation/pr_nat_basic.ma".
17 (* POSITIVE APPLICATION FOR PARTIAL RELOCATION MAPS *************************)
19 (* Constructions with pr_basic **********************************************)
22 lemma pr_pat_basic_lt (m) (n) (i):
23 ninj i ≤ m → @⧣❨i, 𝐛❨m,n❩❩ ≘ i.
24 #m #n #i >(npsucc_pred i) #Hmi
25 /2 width=1 by pr_nat_basic_lt/
29 lemma pr_pat_basic_ge (m) (n) (i):
30 m < ninj i → @⧣❨i, 𝐛❨m,n❩❩ ≘ i+n.
31 #m #n #i >(npsucc_pred i) #Hmi <nrplus_npsucc_sn
32 /3 width=1 by pr_nat_basic_ge, nlt_inv_succ_dx/
35 (* Inversions with pr_basic *************************************************)
37 (*** at_basic_inv_lt *)
38 lemma pr_pat_basic_inv_lt (m) (n) (i) (j):
39 ninj i ≤ m → @⧣❨i, 𝐛❨m,n❩❩ ≘ j → i = j.
40 /3 width=4 by pr_pat_basic_lt, pr_pat_mono/ qed-.
42 (*** at_basic_inv_ge *)
43 lemma pr_pat_basic_inv_ge (m) (n) (i) (j):
44 m < ninj i → @⧣❨i, 𝐛❨m,n❩❩ ≘ j → i+n = j.
45 /3 width=4 by pr_pat_basic_ge, pr_pat_mono/ qed-.