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

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