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1 (**************************************************************************)
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11 (*        v         GNU General Public License Version 2                  *)
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14
15 include "ground/arith/nat_rplus_succ.ma".
16 include "ground/relocation/pr_uni.ma".
17 include "ground/relocation/pr_pat_pat_id.ma".
18
19 (* POSITIVE APPLICATION FOR PARTIAL RELOCATION MAPS *************************)
20
21 (* Constructions with pr_uni ************************************************)
22
23 (*** at_uni *)
24 lemma pr_pat_uni (n) (i):
25       @❨i,𝐮❨n❩❩ ≘ i+n.
26 #n @(nat_ind_succ … n) -n
27 /2 width=5 by pr_pat_next/
28 qed.
29
30 (* Inversions with pr_uni ***************************************************)
31
32 (*** at_inv_uni *)
33 lemma pr_pat_inv_uni (n) (i) (j):
34       @❨i,𝐮❨n❩❩ ≘ j → j = i+n.
35 /2 width=4 by pr_pat_mono/ qed-.