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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/rt_transition/cpm_cpx.ma".
16 include "basic_2/rt_transition/cnr_tdeq.ma".
17 include "basic_2/rt_computation/csx.ma".
18 include "basic_2/rt_computation/cpre.ma".
20 (* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS **********)
22 (* Properties with strong normalization for unbound rt-transition for terms *)
24 (* Basic_1: was just: nf2_sn3 *)
25 lemma cpre_total_csx (h) (G) (L):
26 ∀T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ → ∃T2. ⦃G,L⦄ ⊢ T1 ➡*[h] 𝐍⦃T2⦄.
28 @(csx_ind … H) -T1 #T1 #_ #IHT1
29 elim (cnr_dec_tdeq h G L T1) [ /3 width=3 by ex_intro, cpme_intro/ ] *
31 elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=2 by cpm_fwd_cpx/ ]
32 #T2 * /4 width=3 by cprs_step_sn, ex_intro, cpme_intro/