matita/matita/contribs/lambdadelta/basic_2/etc/referred/lfpr_drops.etc

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  14
  15 include "basic_2/static/lfxs_drops.ma".
  16 include "basic_2/rt_transition/cpm_drops.ma".
  17 include "basic_2/rt_transition/lfpr.ma".
  18
  19 (* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
  20
  21 (* Properties with generic slicing for local environments *******************)
  22
  23 (* Basic_2A1: uses: drop_lpr_trans *)
  24 lemma drops_lfpr_trans: ∀h,G. dedropable_sn (λL. cpm h G L 0).
  25 /3 width=6 by lfxs_liftable_dedropable_sn, cpm_lifts_sn/ qed-.
  26
  27 (* Inversion lemmas with generic slicing for local environments *************)
  28
  29 (* Basic_2A1: uses: lpr_drop_conf *)
  30 lemma lfpr_drops_conf: ∀h,G. dropable_sn (λL. cpm h G L 0).
  31 /2 width=5 by lfxs_dropable_sn/ qed-.
  32
  33 (* Basic_2A1: uses: lpr_drop_trans_O1 *)
  34 lemma lfpr_drops_trans: ∀h,G. dropable_dx (λL. cpm h G L 0).
  35 /2 width=5 by lfxs_dropable_dx/ qed-.
  36
  37 lemma lfpr_inv_lref_pair_sn: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
  38                              ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & ⦃G, K1⦄ ⊢ ➡[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h] V2.
  39 /2 width=3 by lfxs_inv_lref_pair_sn/ qed-.
  40
  41 lemma lfpr_inv_lref_pair_dx: ∀h,G,L1,L2,i. ⦃G, L1⦄ ⊢ ➡[h, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
  42                              ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & ⦃G, K1⦄ ⊢ ➡[h, V1] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h] V2.
  43 /2 width=3 by lfxs_inv_lref_pair_dx/ qed-.