matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_ist_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                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground/relocation/pr_pat_tls.ma".
  16 include "ground/relocation/pr_isi_tls.ma".
  17 include "ground/relocation/pr_ist_tls.ma".
  18 include "ground/relocation/pr_coafter_nat_tls.ma".
  19
  20 (* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
  21
  22 (*** H_coafter_fwd_isid2 *)
  23 definition H_pr_coafter_des_ist_sn_isi: predicate pr_map ≝
  24            λf1. ∀f2,f. f1 ~⊚ f2 ≘ f → 𝐓❨f1❩ → 𝐈❨f❩ → 𝐈❨f2❩.
  25
  26 (* Destructions with pr_ist and pr_isi **************************************)
  27
  28 (*** coafter_fwd_isid2_O_aux *)
  29 corec fact pr_coafter_des_ist_sn_isi_unit_aux:
  30            ∀f1. @❨𝟏, f1❩ ≘ 𝟏 → H_pr_coafter_des_ist_sn_isi f1.
  31 #f1 #H1f1 #f2 #f #H #H2f1 #Hf
  32 cases (pr_pat_inv_unit_bi … H1f1) -H1f1 [ |*: // ] #g1 #H1
  33 lapply (pr_ist_inv_push … H2f1 … H1) -H2f1 #H2g1
  34 cases (H2g1 (𝟏)) #n #Hn
  35 cases (pr_coafter_inv_push_sn … H … H1) -H * #g2 #g #H #H2 #H0
  36 [ lapply (pr_isi_inv_push … Hf … H0) -Hf #Hg
  37   @(pr_isi_push … H2) -H2
  38   /3 width=7 by pr_coafter_tls_sn_tls, pr_pat_unit_succ_tls, pr_ist_tls, pr_isi_tls/
  39 | cases (pr_isi_inv_next … Hf … H0)
  40 ]
  41 qed-.
  42
  43 (*** coafter_fwd_isid2_aux *)
  44 fact pr_coafter_des_ist_sn_isi_aux:
  45      (∀f1. @❨𝟏, f1❩ ≘ 𝟏 → H_pr_coafter_des_ist_sn_isi f1) →
  46      ∀i2,f1. @❨𝟏, f1❩ ≘ i2 → H_pr_coafter_des_ist_sn_isi f1.
  47 #H0 #i2 elim i2 -i2 /2 width=1 by/ -H0
  48 #i2 #IH #f1 #H1f1 #f2 #f #H #H2f1 #Hf
  49 elim (pr_pat_inv_unit_succ … H1f1) -H1f1 [ |*: // ] #g1 #Hg1 #H1
  50 elim (pr_coafter_inv_next_sn … H … H1) -H #g #Hg #H0
  51 @(IH … Hg1 … Hg) /2 width=3 by pr_ist_inv_next, pr_isi_inv_push/ (* * full auto fails *)
  52 qed-.
  53
  54 (*** coafter_fwd_isid2 *)
  55 lemma pr_coafter_des_ist_sn_isi:
  56       ∀f1. H_pr_coafter_des_ist_sn_isi f1.
  57 #f1 #f2 #f #Hf #H cases (H (𝟏))
  58 /3 width=7 by pr_coafter_des_ist_sn_isi_aux, pr_coafter_des_ist_sn_isi_unit_aux/
  59 qed-.