matita/matita/contribs/lambdadelta/basic_2/static/frees_fqup.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground_2/relocation/rtmap_id.ma".
  16 include "basic_2/s_computation/fqup_weight.ma".
  17 include "basic_2/static/frees.ma".
  18
  19 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 (* Notes: this replaces lemma 1400 concluding the "big tree" theorem *)
  24 lemma frees_total: ∀L,T. ∃f. L ⊢ 𝐅*⦃T⦄ ≡ f.
  25 #L #T @(fqup_wf_ind_eq … (⋆) L T) -L -T
  26 #G0 #L0 #T0 #IH #G #L *
  27 [ cases L -L /3 width=2 by frees_atom, ex_intro/
  28   #L #I #V *
  29   [ #s #HG #HL #HT destruct
  30     elim (IH G L (⋆s)) -IH /3 width=2 by frees_sort_gen, fqu_fqup, fqu_drop, lifts_sort, ex_intro/
  31   | * [2: #i ] #HG #HL #HT destruct
  32     [ elim (IH G L (#i)) -IH /3 width=2 by frees_lref, fqu_fqup, ex_intro/
  33     | elim (IH G L V) -IH /3 width=2 by frees_zero, fqu_fqup, fqu_lref_O, ex_intro/
  34     ]
  35   | #l #HG #HL #HT destruct
  36     elim (IH G L (§l)) -IH /3 width=2 by frees_gref_gen, fqu_fqup, fqu_drop, lifts_gref, ex_intro/
  37   ]
  38 | * [ #p ] #I #V #T #HG #HL #HT destruct elim (IH G L V) // #f1 #HV
  39   [ elim (IH G (L.ⓑ{I}V) T) -IH // #f2 #HT
  40     elim (sor_isfin_ex f1 (⫱f2))
  41     /3 width=6 by frees_fwd_isfin, frees_bind, isfin_tl, ex_intro/
  42   | elim (IH G L T) -IH // #f2 #HT
  43     elim (sor_isfin_ex f1 f2)
  44     /3 width=6 by frees_fwd_isfin, frees_flat, ex_intro/
  45   ]
  46 ]
  47 qed-.