1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/dynamic/ypr.ma".
17 (* "BIG TREE" PROPER PARALLEL REDUCTION FOR CLOSURES ************************)
19 inductive ysc (h) (g) (L1) (T1): relation2 lenv term ≝
20 | ysc_fw : ∀L2,T2. ♯{L2, T2} < ♯{L1, T1} → ysc h g L1 T1 L2 T2
21 | ysc_cpr : ∀T2. L1 ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → ysc h g L1 T1 L1 T2
22 | ysc_ssta : ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l+1, T2⦄ → ysc h g L1 T1 L1 T2
23 | ysc_lsubsv: ∀L2. h ⊢ L2 ¡⊑[g] L1 → (L1 = L2 → ⊥) → ysc h g L1 T1 L2 T1
27 "'big tree' proper parallel reduction (closure)"
28 'BTPRedProper h g L1 T1 L2 T2 = (ysc h g L1 T1 L2 T2).
30 (* Basic properties *********************************************************)
32 lemma ysc_ypr: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≻[g] ⦃L2, T2⦄ →
33 h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L2, T2⦄.
34 #h #g #L1 #L2 #T1 #T2 * -L2 -T2 /2 width=1/ /2 width=2/
37 (* Inversion lemmas on "big tree" parallel reduction for closures ***********)
39 lemma ypr_inv_ysc: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L2, T2⦄ →
40 h ⊢ ⦃L1, T1⦄ ≻[g] ⦃L2, T2⦄ ∨ (L1 ➡ L2 ∧ T1 = T2).
41 #h #g #L1 #L2 #T1 #T2 * -L2 -T2 /3 width=1/ /3 width=2/
42 [ #T2 #HT12 elim (term_eq_dec T1 T2) #H destruct /3 width=1/ /4 width=1/
43 | #L2 #HL21 elim (lenv_eq_dec L1 L2) #H destruct /3 width=1/ /4 width=1/