matita/matita/contribs/lambdadelta/ground/relocation/pr_pat_basic.ma

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "ground/relocation/pr_nat_basic.ma".
  16
  17 (* POSITIVE APPLICATION FOR PARTIAL RELOCATION MAPS *************************)
  18
  19 (* Constructions with pr_basic **********************************************)
  20
  21 (*** at_basic_lt *)
  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/
  26 qed.
  27
  28 (*** at_basic_ge *)
  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/
  33 qed.
  34
  35 (* Inversions with pr_basic *************************************************)
  36
  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-.
  41
  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-.