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/cprs_cnr.ma".
16 include "basic_2/rt_computation/cprs_cprs.ma".
17 include "basic_2/rt_computation/cprre.ma".
19 (* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS *********)
21 (* Properties with context-sensitive parallel r-computation for terms ******)
23 lemma cprre_cprs_conf (h) (G) (L) (T):
24 ∀T1. ❨G,L❩ ⊢ T ➡*[h,0] T1 →
25 ∀T2. ❨G,L❩ ⊢ T ➡*𝐍[h,0] T2 → ❨G,L❩ ⊢ T1 ➡*𝐍[h,0] T2.
26 #h #G #L #T0 #T1 #HT01 #T2 * #HT02 #HT2
27 elim (cprs_conf … HT01 … HT02) -T0 #T0 #HT10 #HT20
28 lapply (cprs_inv_cnr_sn … HT20 HT2) -HT20 #H destruct
29 /2 width=1 by cpmre_intro/
32 (* Main properties *********************************************************)
34 (* Basic_1: was: nf2_pr3_confluence *)
35 (* Basic_2A1: was: cpre_mono *)
36 theorem cprre_mono (h) (G) (L) (T):
37 ∀T1. ❨G,L❩ ⊢ T ➡*𝐍[h,0] T1 → ∀T2. ❨G,L❩ ⊢ T ➡*𝐍[h,0] T2 → T1 = T2.
38 #h #G #L #T0 #T1 * #HT01 #HT1 #T2 * #HT02 #HT2
39 elim (cprs_conf … HT01 … HT02) -T0 #T0 #HT10 #HT20
40 >(cprs_inv_cnr_sn … HT10 HT1) -T1
41 >(cprs_inv_cnr_sn … HT20 HT2) -T2 //