matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_teqg.ma

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/syntax/teqg.ma".
  16 include "static_2/s_transition/fqu_length.ma".
  17
  18 (* SUPCLOSURE ***************************************************************)
  19
  20 (* Inversion lemmas with context-free generic equivalence for terms *********)
  21
  22 fact fqu_inv_teqg_aux (S) (b):
  23      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂[b] ❪G2,L2,T2❫ →
  24      G1 = G2 → |L1| = |L2| → T1 ≛[S] T2 → ⊥.
  25 #S #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
  26 [1: #I #G #L #V #_ #H elim (nsucc_inv_refl … H)
  27 |6: #I #G #L #T #U #_ #_ #H elim (nsucc_inv_refl … H)
  28 ]
  29 /2 width=6 by teqg_inv_pair_xy_y, teqg_inv_pair_xy_x/
  30 qed-.
  31
  32 (* Basic_2A1: uses: fqu_inv_eq *)
  33 lemma fqu_inv_teqg (S) (b):
  34       ∀G,L1,L2,T1,T2. ❪G,L1,T1❫ ⬂[b] ❪G,L2,T2❫ →
  35       |L1| = |L2| → T1 ≛[S] T2 → ⊥.
  36 #S #b #G #L1 #L2 #T1 #T2 #H
  37 @(fqu_inv_teqg_aux … H) // (**) (* full auto fails *)
  38 qed-.