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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/reducibility/lcpr_lcpr.ma".
16 include "basic_2/computation/lcprs_cprs.ma".
18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
20 (* Advanced properties ******************************************************)
22 lemma lcprs_strip: ∀L,L1. L ⊢ ➡* L1 → ∀L2. L ⊢ ➡ L2 →
23 ∃∃L0. L1 ⊢ ➡ L0 & L2 ⊢ ➡* L0.
26 (* Main properties **********************************************************)
28 theorem lcprs_conf: ∀L,L1. L ⊢ ➡* L1 → ∀L2. L ⊢ ➡* L2 →
29 ∃∃L0. L1 ⊢ ➡* L0 & L2 ⊢ ➡* L0.
32 theorem lcprs_trans: ∀L1,L. L1 ⊢ ➡* L → ∀L2. L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
35 lemma lcprs_pair: ∀L1,L2. L1 ⊢ ➡* L2 → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
36 ∀I. L1. ⓑ{I} V1 ⊢ ➡* L2. ⓑ{I} V2.
37 #L1 #L2 #H @(lcprs_ind … H) -L2 /2 width=1/
38 #L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
39 @(lcprs_trans … (L.ⓑ{I}V1)) /2 width=1/