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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/computation/lcprs_cprs.ma".
17 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
19 (* Main properties **********************************************************)
21 theorem lcprs_trans: ∀L1,L. L1 ⊢ ➡* L → ∀L2. L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
24 lemma lcprs_pair: ∀L1,L2. L1 ⊢ ➡* L2 → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
25 ∀I. L1. ⓑ{I} V1 ⊢ ➡* L2. ⓑ{I} V2.
26 #L1 #L2 #H @(lcprs_ind … H) -L2 /2 width=1/
27 #L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
28 @(lcprs_trans … (L.ⓑ{I}V1)) /2 width=1/