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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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11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/rt_computation/cprre_csx.ma".
16 include "basic_2/rt_computation/cprre_cprre.ma".
17 include "basic_2/rt_equivalence/cpcs_cprs.ma".
19 (* CONTEXT-SENSITIVE PARALLEL R-EQUIVALENCE FOR TERMS ***********************)
21 (* Properties with strongly normalizing terms for extended rt-transition ****)
23 (* Basic_1: was: cpcs_dec *)
24 lemma csx_cpcs_dec (h) (G) (L):
25 ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 → ∀T2. ❪G,L❫ ⊢ ⬈*𝐒 T2 →
26 Decidable … (❪G,L❫ ⊢ T1 ⬌*[h] T2).
27 #h #G #L #T1 #HT1 #T2 #HT2
28 elim (cprre_total_csx h … HT1) -HT1 #U1 #HTU1
29 elim (cprre_total_csx h … HT2) -HT2 #U2 #HTU2
30 elim (eq_term_dec U1 U2) [ #H destruct | #HnU12 ]
31 [ cases HTU1 -HTU1 #HTU1 #_
32 cases HTU2 -HTU2 #HTU2 #_
33 /3 width=3 by cprs_div, or_introl/
35 elim (cpcs_inv_cprs … H) -H #T0 #HT10 #HT20
36 lapply (cprre_cprs_conf … HT10 … HTU1) -T1 #H1
37 lapply (cprre_cprs_conf … HT20 … HTU2) -T2 #H2
38 /3 width=6 by cprre_mono/