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

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "ground/relocation/pr_isi_id.ma".
  16 include "ground/relocation/pr_coafter_coafter.ma".
  17
  18 (* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
  19
  20 (* Constructions with pr_isi ************************************************)
  21
  22 (*** coafter_isid_sn *)
  23 corec lemma pr_coafter_isi_sn:
  24             ∀f1. 𝐈❨f1❩ → ∀f2. f1 ~⊚ f2 ≘ f2.
  25 #f1 * -f1 #f1 #g1 #Hf1 #H1 #f2
  26 cases (pr_map_split_tl f2) #H2
  27 /3 width=7 by pr_coafter_push, pr_coafter_refl/
  28 qed.
  29
  30 (*** coafter_isid_dx *)
  31 corec lemma pr_coafter_isi_dx:
  32             ∀f2,f. 𝐈❨f2❩ → 𝐈❨f❩ → ∀f1. f1 ~⊚ f2 ≘ f.
  33 #f2 #f * -f2 #f2 #g2 #Hf2 #H2 * -f #f #g #Hf #H #f1
  34 cases (pr_map_split_tl f1) #H1
  35 [ /3 width=7 by pr_coafter_refl/
  36 | @(pr_coafter_next … H1 … H) /3 width=3 by pr_isi_push/
  37 ]
  38 qed.
  39
  40 (* Inversions with pr_isi ***************************************************)
  41
  42 (*** coafter_isid_inv_sn *)
  43 lemma pr_coafter_isi_inv_sn:
  44       ∀f1,f2,f. f1 ~⊚ f2 ≘ f → 𝐈❨f1❩ → f2 ≐ f.
  45 /3 width=6 by pr_coafter_isi_sn, pr_coafter_mono/ qed-.
  46
  47 (*** coafter_isid_inv_dx *)
  48 lemma pr_coafter_isi_inv_dx:
  49       ∀f1,f2,f. f1 ~⊚ f2 ≘ f → 𝐈❨f2❩ → 𝐈❨f❩.
  50 /4 width=4 by pr_eq_id_isi, pr_coafter_isi_dx, pr_coafter_mono/ qed-.