matita/matita/contribs/lambdadelta/basic_2/static/frees_frees.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 "basic_2/static/frees.ma".
  16
  17 (* CONTEXT-SENSITIVE FREE VARIABLES *****************************************)
  18
  19 (* Main inversion lemmas ****************************************************)
  20
  21 theorem frees_mono: ∀L,T,f1. L ⊢ 𝐅*⦃T⦄ ≡ f1 → ∀f2. L ⊢ 𝐅*⦃T⦄ ≡ f2 → f1 ≗ f2.
  22 #L #T #f1 #H elim H -L -T -f1
  23 [ /3 width=2 by frees_inv_atom, isid_inv_eq_repl/
  24 | /4 width=5 by frees_inv_sort, eq_push_inv_isid, isid_inv_eq_repl, eq_trans/
  25 | #I #L #V #f1 #_ #IH #x #H elim (frees_inv_zero … H) -H *
  26   [ #H destruct
  27   | #Z #Y #X #f2 #Hf2 #H1 #H2 destruct /3 width=5 by eq_next/
  28   ]
  29 | #I #L #V #i #f1 #_ #IH #x #H elim (frees_inv_lref … H) -H *
  30   [ #H destruct
  31   | #Z #Y #X #f2 #Hf2 #H1 #H2 destruct /3 width=5 by eq_push/
  32   ]
  33 | /4 width=5 by frees_inv_gref, eq_push_inv_isid, isid_inv_eq_repl, eq_trans/
  34 | #I #L #V #T #p #f1 #f2 #f #_ #_ #Hf #IHV #IHT #g #H elim (frees_inv_bind … H) -H
  35   #g1 #g2 #HV #HT #Hg @(sor_mono … Hf) -Hf
  36   /5 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1, tl_eq_repl/ (**) (* full auto too slow *)
  37 | #I #L #V #T #f1 #f2 #f #_ #_ #Hf #IHV #IHT #g #H elim (frees_inv_flat … H) -H
  38   #g1 #g2 #HV #HT #Hg @(sor_mono … Hf) -Hf
  39   /4 width=3 by sor_eq_repl_fwd2, sor_eq_repl_fwd1/ (**) (* full auto too slow *)
  40 ]
  41 qed-.