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/reducibility/cpr_cpr.ma".
16 include "Basic_2/computation/cprs_lcpr.ma".
18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
20 (* Advanced properties ******************************************************)
22 lemma cprs_abbr_dx: ∀L,V1,V2. L ⊢ V1 ➡ V2 → ∀T1,T2. L. ⓓV1 ⊢ T1 ➡* T2 →
23 L ⊢ ⓓV1. T1 ➡* ⓓV2. T2.
24 #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cprs_ind_dx … HT12) -T1
26 | #T1 #T #HT1 #_ #IHT1
27 @(cprs_strap2 … IHT1) -IHT1 /2 width=1/
31 lemma cpr_abbr: ∀L,V1,V2. L ⊢ V1 ➡ V2 → ∀T1,T2. L. ⓓV1 ⊢ T1 ➡ T2 →
32 L ⊢ ⓓV1. T1 ➡* ⓓV2. T2.
35 (* Basic_1: was only: pr3_pr2_pr3_t *)
36 lemma lcpr_cprs_trans: ∀L1,L2. L1 ⊢ ➡ L2 →
37 ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
38 #L1 #L2 #HL12 #T1 #T2 #H @(cprs_ind … H) -T2 //
39 #T #T2 #_ #HT2 #IHT2 /3 width=5/
42 (* Main propertis ***********************************************************)
44 (* Basic_1: was: pr3_t *)
45 theorem cprs_trans: ∀L,T1,T. L ⊢ T1 ➡* T → ∀T2. L ⊢ T ➡* T2 → L ⊢ T1 ➡* T2.
48 (* Basic_1: was: pr3_confluence *)
49 theorem cprs_conf: ∀L,T1,T. L ⊢ T ➡* T1 → ∀T2. L ⊢ T ➡* T2 →
50 ∃∃T0. L ⊢ T1 ➡* T0 & L ⊢ T2 ➡* T0.