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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/rt_transition/cpm_cpx.ma".
16 include "basic_2/rt_transition/cnr_teqx.ma".
17 include "basic_2/rt_computation/csx.ma".
18 include "basic_2/rt_computation/cprre.ma".
20 (* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS **********)
22 (* Properties with strongly normalizing terms for extended rt-transition ****)
24 (* Basic_1: was just: nf2_sn3 *)
25 (* Basic_2A1: was: csx_cpre *)
26 lemma cprre_total_csx (h) (G) (L):
27 ∀T1. ❨G,L❩ ⊢ ⬈*𝐒 T1 → ∃T2. ❨G,L❩ ⊢ T1 ➡*𝐍[h,0] T2.
29 @(csx_ind … H) -T1 #T1 #_ #IHT1
30 elim (cnr_dec_teqx h G L T1) [ /3 width=3 by ex_intro, cpmre_intro/ ] *
32 elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=3 by cpm_fwd_cpx/ ]
33 #T2 * /4 width=3 by cprs_step_sn, ex_intro, cpmre_intro/