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14
15 include "ground/relocation/pr_pat_pat.ma".
16 include "ground/relocation/tr_pat.ma".
17 include "ground/relocation/tr_pap.ma".
18
19 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
20
21 (* Constructions with pr_pat ***********************************************)
22
23 (*** at_total *)
24 lemma tr_pat_total: ∀i1,f. @❨i1,𝐭❨f❩❩ ≘ f@❨i1❩.
25 #i1 elim i1 -i1
26 [ * // | #i #IH * /3 width=1 by tr_pat_succ_sn/ ]
27 qed.
28
29 (* Inversions with pr_pat ***************************************************)
30
31 (*** at_inv_total *)
32 lemma tr_pat_inv_total (f):
33       ∀i1,i2. @❨i1, 𝐭❨f❩❩ ≘ i2 → f@❨i1❩ = i2.
34 /2 width=6 by pr_pat_mono/ qed-.