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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/reducibility/cpr_delift.ma".
16 include "basic_2/reducibility/cpr_cpr.ma".
17 include "basic_2/computation/cprs.ma".
19 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
21 (* Properties on inverse basic term relocation ******************************)
23 lemma cprs_zeta_delift: ∀L,V,T1,T2. L.ⓓV ⊢ T1 ▼*[O, 1] ≡ T2 → L ⊢ ⓓV.T1 ➡* T2.
24 #L #V #T1 #T2 * #T #HT1 #HT2
25 @(cprs_strap2 … (ⓓV.T)) [ /3 width=3/ | @inj /3 width=3/ ] (**) (* explicit constructor, /5 width=3/ is too slow *)
28 (* Basic_1: was only: pr3_gen_cabbr *)
29 lemma thin_cprs_delift_conf: ∀L,U1,U2. L ⊢ U1 ➡* U2 →
30 ∀K,d,e. L ▼*[d, e] ≡ K → ∀T1. L ⊢ U1 ▼*[d, e] ≡ T1 →
31 ∃∃T2. K ⊢ T1 ➡* T2 & L ⊢ U2 ▼*[d, e] ≡ T2.
32 #L #U1 #U2 #H @(cprs_ind … H) -U2 /2 width=3/
33 #U #U2 #_ #HU2 #IHU1 #K #d #e #HLK #T1 #HTU1
34 elim (IHU1 … HLK … HTU1) -U1 #T #HT1 #HUT
35 elim (thin_cpr_delift_conf … HU2 … HLK … HUT) -U -HLK /3 width=3/