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/lfpr_lfpr.ma".
16 include "basic_2/computation/lfprs_cprs.ma".
18 (* FOCALIZED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *********************)
20 (* Advanced properties ******************************************************)
22 lemma lfprs_strip: ∀L,L1. ⦃L⦄ ➡* ⦃L1⦄ → ∀L2. ⦃L⦄ ➡ ⦃L2⦄ →
23 ∃∃L0. ⦃L1⦄ ➡ ⦃L0⦄ & ⦃L2⦄ ➡* ⦃L0⦄.
26 (* Main properties **********************************************************)
28 theorem lfprs_conf: ∀L,L1. ⦃L⦄ ➡* ⦃L1⦄ → ∀L2. ⦃L⦄ ➡* ⦃L2⦄ →
29 ∃∃L0. ⦃L1⦄ ➡* ⦃L0⦄ & ⦃L2⦄ ➡* ⦃L0⦄.
32 theorem lfprs_trans: ∀L1,L. ⦃L1⦄ ➡* ⦃L⦄ → ∀L2. ⦃L⦄ ➡* ⦃L2⦄ → ⦃L1⦄ ➡* ⦃L2⦄.
35 lemma lfprs_pair: ∀L1,L2. ⦃L1⦄ ➡* ⦃L2⦄ → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
36 ∀I. ⦃L1. ⓑ{I} V1⦄ ➡* ⦃L2. ⓑ{I} V2⦄.
37 #L1 #L2 #H @(lfprs_ind … H) -L2 /2 width=1/
38 #L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
39 @(lfprs_trans … (L.ⓑ{I}V1)) /2 width=1/