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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/relocation/lex_tc.ma".
16 include "basic_2/rt_computation/lpxs.ma".
17 include "basic_2/rt_computation/cpxs_lpx.ma".
19 (* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENVIRONMENTS *******************)
21 (* Properties with unbound rt-transition for local environments *************)
23 (* Basic_2A1: was: lpxs_strap1 *)
24 lemma lpxs_step_dx: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈*[h] L →
25 ∀L2. ⦃G, L⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
26 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
28 (* Basic_2A1: was: lpxs_strap2 *)
29 lemma lpxs_step_sn: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈[h] L →
30 ∀L2. ⦃G, L⦄ ⊢ ⬈*[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
31 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_sn/ qed-.