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

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   3 (*      ||M||                                                             *)
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  14
  15 include "ground/relocation/pr_nexts_eq.ma".
  16 include "ground/relocation/tr_nexts.ma".
  17
  18 (* TOTAL RELOCATION MAPS ****************************************************)
  19
  20 (* Constructions with pr_eq and stream_eq ***********************************)
  21
  22 corec lemma eq_tr_inj_bi (f1) (f2): f1 ≗ f2 → 𝐭❨f1❩ ≐ 𝐭❨f2❩.
  23 * -f1 -f2 #p1 #p2 #f1 #f2 * -p2 #H
  24 cases p1 -p1
  25 [ @pr_eq_push /2 width=5 by/
  26 | #p @pr_eq_next [3:|*: //]
  27   cases tr_inj_fold cases tr_inj_fold
  28   /3 width=5 by stream_eq_cons/
  29 ]
  30 qed.
  31
  32 (* Inversions with pr_eq and stream_eq **************************************)
  33
  34 corec lemma eq_inv_tr_inj_bi (f1) (f2): 𝐭❨f1❩ ≐ 𝐭❨f2❩ → f1 ≗ f2.
  35 cases f1 -f1 #p1 #f1 cases f2 -f2 #p2 #f2
  36 cases tr_inj_unfold cases tr_inj_unfold #H
  37 cases (pr_eq_inv_nexts_push_bi … H) -H #H1 #H2
  38 @stream_eq_cons /2 width=1 by/
  39 qed-.