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

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/syntax/tdeq.ma".
  16 include "static_2/s_transition/fqu_length.ma".
  17
  18 (* SUPCLOSURE ***************************************************************)
  19
  20 (* Inversion lemmas with context-free degree-based equivalence for terms ****)
  21
  22 fact fqu_inv_tdeq_aux: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
  23                        G1 = G2 → |L1| = |L2| → T1 ≛[h, o] T2 → ⊥.
  24 #h #o #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
  25 [1: #I #G #L #V #_ #H elim (succ_inv_refl_sn … H)
  26 |6: #I #G #L #T #U #_ #_ #H elim (succ_inv_refl_sn … H)
  27 ]
  28 /2 width=6 by tdeq_inv_pair_xy_y, tdeq_inv_pair_xy_x/
  29 qed-.
  30
  31 (* Basic_2A1: uses: fqu_inv_eq *)
  32 lemma fqu_inv_tdeq: ∀h,o,b,G,L1,L2,T1,T2. ⦃G, L1, T1⦄ ⊐[b] ⦃G, L2, T2⦄ →
  33                     |L1| = |L2| → T1 ≛[h, o] T2 → ⊥.
  34 #h #o #b #G #L1 #L2 #T1 #T2 #H
  35 @(fqu_inv_tdeq_aux … H) // (**) (* full auto fails *)
  36 qed-.