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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/notation/relations/btpred_8.ma".
16 include "basic_2/relocation/fsup.ma".
17 include "basic_2/reduction/lpr.ma".
18 include "basic_2/dynamic/lsubsv.ma".
20 (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
22 inductive ypr (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
23 | ypr_fsup : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ypr h g G1 L1 T1 G2 L2 T2
24 | ypr_lpr : ∀L2. ⦃G1, L1⦄ ⊢ ➡ L2 → ypr h g G1 L1 T1 G1 L2 T1
25 | ypr_cpr : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → ypr h g G1 L1 T1 G1 L1 T2
26 | ypr_ssta : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → ypr h g G1 L1 T1 G1 L1 T2
27 | ypr_lsubsv: ∀L2. G1 ⊢ L2 ¡⊑[h, g] L1 → ypr h g G1 L1 T1 G1 L2 T1
31 "'big tree' parallel reduction (closure)"
32 'BTPRed h g G1 L1 T1 G2 L2 T2 = (ypr h g G1 L1 T1 G2 L2 T2).
34 (* Basic properties *********************************************************)
36 lemma ypr_refl: ∀h,g. tri_reflexive … (ypr h g).