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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_fqup.ma".
16 include "basic_2/rt_transition/lfpr.ma".
18 (* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
20 (* Advanced properties ******************************************************)
23 (* Basic_2A1: uses: lpr_refl *)
24 lemma lfpr_refl: ∀h,G,T. reflexive … (lfpr h G T).
25 /2 width=1 by lfxs_refl/ qed.
27 (* Basic_2A1: uses: lpr_pair *)
28 lemma lfpr_pair_refl: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 →
29 ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ➡[h, T] L.ⓑ{I}V2.
30 /2 width=1 by lfxs_pair_refl/ qed.
32 (* Advanced inversion lemmas ************************************************)
34 lemma lfpr_inv_bind_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 →
35 ∧∧ ⦃G, L1⦄ ⊢ ➡[h, V] L2 & ⦃G, L1.ⓧ⦄ ⊢ ➡[h, T] L2.ⓧ.
36 /2 width=3 by lfxs_inv_bind_void/ qed-.
38 (* Advanced forward lemmas **************************************************)
40 lemma lfpr_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T.
41 ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 → ⦃G, L1.ⓧ⦄ ⊢ ➡[h, T] L2.ⓧ.
42 /2 width=4 by lfxs_fwd_bind_dx_void/ qed-.