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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/static/ssta.ma".
16 include "basic_2/reducibility/cpr.ma".
18 (* EXTENDED PARALLEL REDUCTION ON TERMS *************************************)
20 definition xpr: ∀h. sd h → lenv → relation term ≝
21 λh,g,L,T1,T2. L ⊢ T1 ➡ T2 ∨ ∃l. ⦃h, L⦄ ⊢ T1 •[g, l + 1] T2.
24 "extended parallel reduction (term)"
25 'XPRed h g L T1 T2 = (xpr h g L T1 T2).
27 (* Basic properties *********************************************************)
29 lemma cpr_xpr: ∀h,g,L,T1,T2. L ⊢ T1 ➡ T2 → ⦃h, L⦄ ⊢ T1 ➸[g] T2.
32 lemma ssta_xpr: ∀h,g,L,T1,T2,l. ⦃h, L⦄ ⊢ T1 •[g, l + 1] T2 → ⦃h, L⦄ ⊢ T1 ➸[g] T2.
35 lemma xpr_refl: ∀h,g,L,T. ⦃h, L⦄ ⊢ T ➸[g] T.