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

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   3 (*      ||M||                                                             *)
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  13 (**************************************************************************)
  14
  15 include "ground/relocation/pr_isi.ma".
  16 include "ground/relocation/pr_sdj.ma".
  17
  18 (* DISJOINTNESS FOR PARTIAL RELOCATION MAPS *********************************)
  19
  20 (* Constructions with pr_isi ************************************************)
  21
  22 (*** sdj_isid_dx *)
  23 corec lemma pr_sdj_isi_dx:
  24             ∀f2. 𝐈❨f2❩ → ∀f1. f1 ∥ f2.
  25 #f2 * -f2
  26 #f2 #g2 #Hf2 #H2 #f1 cases (pr_map_split_tl f1) *
  27 /3 width=5 by pr_sdj_next_push, pr_sdj_push_bi/
  28 qed.
  29
  30 (*** sdj_isid_sn *)
  31 corec lemma pr_sdj_isi_sn:
  32             ∀f1. 𝐈❨f1❩ → ∀f2. f1 ∥ f2.
  33 #f1 * -f1
  34 #f1 #g1 #Hf1 #H1 #f2 cases (pr_map_split_tl f2) *
  35 /3 width=5 by pr_sdj_push_next, pr_sdj_push_bi/
  36 qed.
  37
  38 (* Inversions with pr_isi ***************************************************)
  39
  40 (*** sdj_inv_refl *)
  41 corec lemma pr_sdj_inv_refl:
  42             ∀f. f ∥ f →  𝐈❨f❩.
  43 #f cases (pr_map_split_tl f) #Hf #H
  44 [ lapply (pr_sdj_inv_push_bi … H … Hf Hf) -H /3 width=3 by pr_isi_push/
  45 | elim (pr_sdj_inv_next_bi … H … Hf Hf)
  46 ]
  47 qed-.