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14
15 include "Basic_2/reducibility/lcpr_cpr.ma".
16 include "Basic_2/computation/cprs.ma".
17 include "Basic_2/computation/lcprs.ma".
18
19 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
20
21 (* Advanced properties ******************************************************)
22
23 lemma lcprs_pair_dx: ∀I,L1,L2. L1 ⊢ ➡ L2 → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
24                      L1. ⓑ{I} V1 ⊢ ➡* L2. ⓑ{I} V2.
25 #I #L1 #L2 #HL12 #V1 #V2 #H @(cprs_ind … H) -V2
26 /3 width=1/ /3 width=5/
27 qed.