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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 *)
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15 include "basic_2/i_static/tc_lfxs_fqup.ma".
16 include "basic_2/rt_computation/lfpxs.ma".
18 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
20 (* Advanced properties ******************************************************)
22 (* Basic_2A1: uses: lpxs_refl *)
23 lemma lfpxs_refl: ∀h,G,T. reflexive … (lfpxs h G T).
24 /2 width=1 by tc_lfxs_refl/ qed.
26 (* Advanced forward lemmas **************************************************)
28 lemma lfpxs_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
29 ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈*[h, T] L2.ⓑ{I}V.
30 /2 width=2 by tc_lfxs_fwd_bind_dx/ qed-.
32 (* Advanced eliminators *****************************************************)
34 (* Basic_2A1: uses: lpxs_ind *)
35 lemma lfpxs_ind_sn: ∀h,G,L1,T. ∀R:predicate lenv. R L1 →
36 (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → R L → R L2) →
37 ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L2.
38 #h #G @tc_lfxs_ind_sn // (**) (* auto fails *)
41 (* Basic_2A1: uses: lpxs_ind_dx *)
42 lemma lfpxs_ind_dx: ∀h,G,L2,T. ∀R:predicate lenv. R L2 →
43 (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → R L → R L1) →
44 ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L1.
45 #h #G @tc_lfxs_ind_dx // (**) (* auto fails *)