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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 *)
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15 include "ground/arith/pnat_lt.ma".
16 include "ground/relocation/tr_pushs.ma".
17 include "ground/relocation/tr_pap_pn.ma".
19 (* POSITIVE APPLICATION FOR TOTAL RELOCATION MAPS ***************************)
21 (* Constructions with tr_pushs **********************************************)
23 lemma tr_pap_pushs_le (n) (p) (f):
24 p < ↑n → p = (⫯*[n]f)@❨p❩.
25 #n @(nat_ind_succ … n) -n
27 elim (plt_inv_unit_dx … H0)
29 [ #f #H0 <tr_pushs_succ //
30 | #p #f <npsucc_succ #H0
31 lapply (plt_inv_succ_bi … H0) -H0 #H0
32 lapply (IH … f H0) -IH -H0 #H0
33 <tr_pushs_succ <tr_pap_push //