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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/reducibility/ltpr_tps.ma".
16 include "basic_2/reducibility/cpr_ltpss.ma".
17 include "basic_2/reducibility/lcpr.ma".
18 include "basic_2/computation/cprs.ma".
20 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
22 (* Properties concerning context-sensitive parallel reduction on lenv's *****)
24 lemma ltpr_tpss_trans: ∀L1,L2. L1 ➡ L2 → ∀T1,T2,d,e. L2 ⊢ T1 ▶* [d, e] T2 →
25 ∃∃T. L1 ⊢ T1 ▶* [d, e] T & L1 ⊢ T ➡* T2.
26 #L1 #L2 #HL12 #T1 #T2 #d #e #H @(tpss_ind … H) -T2
28 | #T #T2 #_ #HT2 * #T0 #HT10 #HT0
29 elim (ltpr_tps_trans … HT2 … HL12) -L2 #T3 #HT3 #HT32
30 @(ex2_1_intro … HT10) -T1 (**) (* explicit constructors *)
31 @(cprs_strap1 … T3 …) /2 width=1/ -HT32
32 @(cprs_strap1 … HT0) -HT0 /3 width=3/
36 (* Basic_1: was just: pr3_pr0_pr2_t *)
37 lemma ltpr_cpr_trans: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡* T2.
38 #L1 #L2 #HL12 #T1 #T2 * #T #HT1
39 <(ltpr_fwd_length … HL12) #HT2
40 elim (ltpr_tpss_trans … HL12 … HT2) -L2 /3 width=3/
43 (* Basic_1: was just: pr3_pr2_pr2_t *)
44 lemma lcpr_cpr_trans: ∀L1,L2. L1 ⊢ ➡ L2 → ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡* T2.