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14
15 include "basic_2/reducibility/cpr_tpss.ma".
16 include "basic_2/computation/cprs.ma".
17
18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
19
20 (* Properties on partial unfold for terms ***********************************)
21
22 lemma cprs_tpss_trans: ∀L,T1,T. L ⊢ T1 ➡* T →
23                        ∀T2,d,e. L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡* T2.
24 #L #T1 #T #H @(cprs_ind … H) -T /2 width=3/ /3 width=5/
25 qed.
26
27 lemma cprs_tps_trans: ∀L,T1,T. L ⊢ T1 ➡* T →
28                       ∀T2,d,e. L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ➡* T2.
29 /3 width=5 by inj, cprs_tpss_trans/ qed. (**) (* auto too slow without trace *)
30
31 lemma cprs_tpss_conf: ∀L,T0,T1. L ⊢ T0 ➡* T1 →
32                       ∀T2,d,e. L ⊢ T0 ▶* [d, e] T2 →
33                       ∃∃T. L ⊢ T1 ▶* [d, e] T & L ⊢ T2 ➡* T.
34 #L #T0 #T1 #H @(cprs_ind … H) -T1 /2 width=3/
35 #T #T1 #_ #HT1 #IHT0 #T2 #d #e #HT02
36 elim (IHT0 … HT02) -T0 #T0 #HT0 #HT20
37 elim (cpr_tpss_conf … HT1 … HT0) -T /3 width=5/
38 qed-.