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

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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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_coafter_nat_tls.ma".
  17
  18 (* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
  19
  20 (* Constructions with pr_pat and pr_tls *************************************)
  21
  22 (* Note: this does not require ↑ first and second j *)
  23 (*** coafter_tls_succ *)
  24 lemma pr_coafter_tls_tl_tls:
  25       ∀g2,g1,g. g2 ~⊚ g1 ≘ g →
  26       ∀j. @❨𝟏, g2❩ ≘ j → ⫰*[j]g2 ~⊚ ⫰g1 ≘ ⫰*[j]g.
  27 #g2 #g1 #g #Hg #j #Hg2
  28 lapply (pr_nat_pred_bi … Hg2) -Hg2 #Hg2
  29 lapply (pr_coafter_tls_bi_tls … Hg2 … Hg) -Hg #Hg
  30 lapply (pr_pat_unit_succ_tls … Hg2) -Hg2 #H
  31 elim (pr_pat_inv_unit_bi … H) -H [ |*: // ] #f2 #H2
  32 elim (pr_coafter_inv_push_sn … Hg … H2) -Hg * #f1 #f #Hf #H1 #H0
  33 >(npsucc_pred j) <pr_tls_succ <pr_tls_succ //
  34 qed.
  35
  36 (* Note: parked for now
  37 lemma coafter_fwd_xpx_pushs:
  38       ∀g2,f1,g,i,j. @❨i, g2❩ ≘ j → g2 ~⊚ ⫯*[i]⫯f1 ≘ g →
  39       ∃∃f.  ⫰*[↑j]g2 ~⊚ f1 ≘ f & ⫯*[j]⫯f = g.
  40 #g2 #g1 #g #i #j #Hg2 <pushs_xn #Hg(coafter_fwd_pushs … Hg Hg2) #f #H0 destruct
  41 lapply (coafter_tls … Hg2 Hg) -Hg <tls_pushs <tls_pushs #Hf
  42 lapply (at_inv_tls … Hg2) -Hg2 #H
  43 lapply (coafter_eq_repl_fwd2 … Hf … H) -H -Hf #Hf
  44 elim (coafter_inv_ppx … Hf) [|*: // ] -Hf #g #Hg #H destruct
  45 /2 width=3 by ex2_intro/
  46 qed-.
  47
  48 lemma coafter_fwd_xnx_pushs:
  49       ∀g2,f1,g,i,j. @❨i, g2❩ ≘ j → g2 ~⊚ ⫯*[i]↑f1 ≘ g →
  50       ∃∃f. ⫰*[↑j]g2 ~⊚ f1 ≘ f & ⫯*[j] ↑f = g.
  51 #g2 #g1 #g #i #j #Hg2 #Hg
  52 elim (coafter_fwd_pushs … Hg Hg2) #f #H0 destruct
  53 lapply (coafter_tls … Hg2 Hg) -Hg <tls_pushs <tls_pushs #Hf
  54 lapply (at_inv_tls … Hg2) -Hg2 #H
  55 lapply (coafter_eq_repl_fwd2 … Hf … H) -H -Hf #Hf
  56 elim (coafter_inv_pnx … Hf) [|*: // ] -Hf #g #Hg #H destruct
  57 /2 width=3 by ex2_intro/
  58 qed-.
  59 *)