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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "Basic_2/reducibility/cpr.ma".
17 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
19 (* Basic_1: includes: pr3_pr2 *)
20 definition cprs: lenv → relation term ≝
23 interpretation "context-sensitive parallel computation (term)"
24 'PRedStar L T1 T2 = (cprs L T1 T2).
26 (* Basic eliminators ********************************************************)
28 lemma cprs_ind: ∀L,T1. ∀R:predicate term. R T1 →
29 (∀T,T2. L ⊢ T1 ➡* T → L ⊢ T ➡ T2 → R T → R T2) →
30 ∀T2. L ⊢ T1 ➡* T2 → R T2.
31 #L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
34 axiom cprs_ind_dx: ∀L,T2. ∀R:predicate term. R T2 →
35 (∀T1,T. L ⊢ T1 ➡ T → L ⊢ T ➡* T2 → R T → R T1) →
36 ∀T1. L ⊢ T1 ➡* T2 → R T1.
38 (* Basic properties *********************************************************)
40 (* Basic_1: was: pr3_refl *)
41 lemma cprs_refl: ∀L,T. L ⊢ T ➡* T.
44 lemma cprs_strap1: ∀L,T1,T,T2.
45 L ⊢ T1 ➡* T → L ⊢ T ➡ T2 → L ⊢ T1 ➡* T2.
48 (* Basic_1: was: pr3_step *)
49 lemma cprs_strap2: ∀L,T1,T,T2.
50 L ⊢ T1 ➡ T → L ⊢ T ➡* T2 → L ⊢ T1 ➡* T2.
53 (* Note: it does not hold replacing |L1| with |L2| *)
54 lemma cprs_lsubs_conf: ∀L1,T1,T2. L1 ⊢ T1 ➡* T2 →
55 ∀L2. L1 [0, |L1|] ≼ L2 → L2 ⊢ T1 ➡* T2.
59 (* Basic_1: removed theorems 2: clear_pr3_trans pr3_cflat *)