1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/rt_computation/cpmre_aaa.ma".
16 include "basic_2/rt_computation/cprre_cprre.ma".
17 include "basic_2/rt_equivalence/cpes.ma".
18 include "basic_2/dynamic/cnv_cpmre.ma".
20 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
22 (* Properties with t-bound rt-equivalence for terms *************************)
24 lemma cnv_cpes_dec (h) (a) (n1) (n2) (G) (L):
25 ∀T1. ❨G,L❩ ⊢ T1 ![h,a] → ∀T2. ❨G,L❩ ⊢ T2 ![h,a] →
26 Decidable … (❨G,L❩ ⊢ T1 ⬌*[h,n1,n2] T2).
27 #h #a #n1 #n2 #G #L #T1 #HT1 #T2 #HT2
28 elim (cnv_fwd_aaa … HT1) #A1 #HA1
29 elim (cnv_fwd_aaa … HT2) #A2 #HA2
30 elim (cpmre_total_aaa h n1 … HA1) -HA1 #U1 #HTU1
31 elim (cpmre_total_aaa h n2 … HA2) -HA2 #U2 #HTU2
32 elim (eq_term_dec U1 U2) [ #H destruct | #HnU12 ]
33 [ cases HTU1 -HTU1 #HTU1 #_
34 cases HTU2 -HTU2 #HTU2 #_
35 /3 width=3 by cpms_div, or_introl/
36 | @or_intror * #T0 #HT10 #HT20
37 lapply (cnv_cpmre_cpms_conf … HT1 … HT10 … HTU1) -T1 #H1
38 lapply (cnv_cpmre_cpms_conf … HT2 … HT20 … HTU2) -T2 #H2
39 /3 width=6 by cprre_mono/