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/notation/relations/btpredproper_8.ma".
16 include "basic_2/relocation/lleq.ma".
17 include "basic_2/computation/fpbs.ma".
19 (* ATOMIC "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************)
21 inductive fpbc (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
22 | fpbc_fqup: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → fpbc h g G1 L1 T1 G2 L2 T2
23 | fpbc_cpxs: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → fpbc h g G1 L1 T1 G1 L1 T2
24 | fpbc_lpxs: ∀L2. ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[0, T1] L2 → ⊥) → fpbc h g G1 L1 T1 G1 L2 T1
28 "'big tree' proper parallel reduction (closure)"
29 'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbc h g G1 L1 T1 G2 L2 T2).
31 (* Basic properties *********************************************************)
33 lemma cprs_fpbc: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
34 ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
35 /3 width=1 by fpbc_cpxs, cprs_cpxs/ qed.
37 lemma lprs_fpbc: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → (L1 ⋕[0, T] L2 → ⊥) →
38 ⦃G, L1, T⦄ ≻[h, g] ⦃G, L2, T⦄.
39 /3 width=1 by fpbc_lpxs, lprs_lpxs/ qed.
41 (* Basic forward lemmas *****************************************************)
43 lemma fpbc_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
44 ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
45 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
46 /3 width=1 by lpxs_fpbs, cpxs_fpbs, fqup_fpbs/