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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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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".
19 (* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
21 (* Properties with generic slicing for local environments *******************)
23 lemma drops_lfpr_trans: ∀h,G. dedropable_sn (cpm 0 h G).
24 /3 width=6 by lfxs_liftable_dedropable, cpm_lifts/ qed-.
26 (* Inversion lemmas with generic slicing for local environments *************)
28 lemma lfpr_drops_conf: ∀h,G. dropable_sn (cpm 0 h G).
29 /2 width=5 by lfxs_dropable_sn/ qed-.
31 lemma lfpr_drops_trans: ∀h,G. dropable_dx (cpm 0 h G).
32 /2 width=5 by lfxs_dropable_dx/ qed-.
34 lemma lfpr_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-.
38 lemma lfpr_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-.