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14
15 include "basic_2/reducibility/tpr_tpr.ma".
16 include "basic_2/computation/tprs.ma".
17
18 (* CONTEXT-FREE PARALLEL COMPUTATION ON TERMS *******************************)
19
20 (* Advanced properties ******************************************************)
21
22 (* Basic_1: was: pr1_strip *)
23 lemma tprs_strip: ∀T1,T. T ➡* T1 → ∀T2. T ➡ T2 →
24                   ∃∃T0. T1 ➡ T0 & T2 ➡* T0.
25 /3 width=3 by TC_strip1, tpr_conf/ qed.
26
27 (* Main propertis ***********************************************************)
28
29 (* Basic_1: was: pr1_confluence *)
30 theorem tprs_conf: confluent … tprs.
31 /3 width=3/ qed.
32
33 (* Basic_1: was: pr1_t *)
34 theorem tprs_trans: Transitive … tprs.
35 /2 width=3/ qed.
36
37 (* Basic_1: was: pr1_comp *)
38 lemma tprs_pair: ∀I,V1,V2. V1 ➡* V2 → ∀T1,T2. T1 ➡* T2 →
39                  ②{I} V1. T1 ➡* ②{I} V2. T2.
40 #I #V1 #V2 #H @(tprs_ind … H) -V2 /2 width=1/
41 #V #V2 #_ #HV2 #IHV1 #T1 #T2 #HT12
42 @(tprs_trans … (②{I}V.T2)) /2 width=1/
43 qed.