matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_drops.ma

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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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 "basic_2/static/lfxs_drops.ma".
  16 include "basic_2/rt_transition/cpx_drops.ma".
  17 include "basic_2/rt_transition/lfpx.ma".
  18
  19 (* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
  20
  21 (* Properties with generic slicing for local environments *******************)
  22
  23 lemma drops_lfpx_trans: ∀h,G. dedropable_sn (cpx h G).
  24 /3 width=6 by lfxs_liftable_dedropable_sn, cpx_lifts_sn/ qed-.
  25
  26 (* Inversion lemmas with generic slicing for local environments *************)
  27
  28 lemma lfpx_drops_conf: ∀h,G. dropable_sn (cpx h G).
  29 /2 width=5 by lfxs_dropable_sn/ qed-.
  30
  31 lemma lfpx_drops_trans: ∀h,G. dropable_dx (cpx h G).
  32 /2 width=5 by lfxs_dropable_dx/ qed-.
  33
  34 lemma lfpx_inv_lref_sn: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 →
  35                         ∃∃K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 & ⦃G, K1⦄ ⊢ ⬈[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2.
  36 /2 width=3 by lfxs_inv_lref_sn/ qed-.
  37
  38 lemma lfpx_inv_lref_dx: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≡ K2.ⓑ{I}V2 →
  39                         ∃∃K1,V1. ⬇*[i] L1 ≡ K1.ⓑ{I}V1 & ⦃G, K1⦄ ⊢ ⬈[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2.
  40 /2 width=3 by lfxs_inv_lref_dx/ qed-.