--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/computation/ltprs.ma".
+include "basic_2/dynamic/lsubsv.ma".
+
+(* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************)
+
+axiom yprs: ∀h. sd h → bi_relation lenv term.
+
+interpretation "'big tree' parallel computation (closure)"
+ 'BTPRedStar h g L1 T1 L2 T2 = (yprs h g L1 T1 L2 T2).
+
+axiom cprs_yprs: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
+
+axiom sstas_yprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 →
+ h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
+
+axiom lsubsv_yprs: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[g] L1 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄.
+
+axiom ltpr_cprs_yprs: ∀h,g,L1,L2,T1,T2. L1 ➡ L2 → L2 ⊢ T1 ➡* T2 →
+ h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
+
+axiom ygt: ∀h. sd h → bi_relation lenv term.
+
+interpretation "'big tree' proper parallel computation (closure)"
+ 'BTPRedStarProper h g L1 T1 L2 T2 = (ygt h g L1 T1 L2 T2).
+
+axiom fw_ygt: ∀h,g,L1,L2,T1,T2. ♯{L2, T2} < ♯{L1, T1} → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.
+
+axiom ygt_yprs_trans: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ >[g] ⦃L, T⦄ →
+ h ⊢ ⦃L, T⦄ ≥[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.
+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/computation/ltprs.ma".
-include "basic_2/dynamic/lsubsv.ma".
-
-(* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************)
-
-axiom yprs: ∀h. sd h → bi_relation lenv term.
-
-interpretation "'big tree' parallel computation (closure)"
- 'BTPRedStar h g L1 T1 L2 T2 = (yprs h g L1 T1 L2 T2).
-
-axiom cprs_yprs: ∀h,g,L,T1,T2. L ⊢ T1 ➡* T2 → h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
-
-axiom sstas_yprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 →
- h ⊢ ⦃L, T1⦄ ≥[g] ⦃L, T2⦄.
-
-axiom lsubsv_yprs: ∀h,g,L1,L2,T. h ⊢ L2 ¡⊑[g] L1 → h ⊢ ⦃L1, T⦄ ≥[g] ⦃L2, T⦄.
-
-axiom ltpr_cprs_yprs: ∀h,g,L1,L2,T1,T2. L1 ➡ L2 → L2 ⊢ T1 ➡* T2 →
- h ⊢ ⦃L1, T1⦄ ≥[g] ⦃L2, T2⦄.
-
-axiom ygt: ∀h. sd h → bi_relation lenv term.
-
-interpretation "'big tree' proper parallel computation (closure)"
- 'BTPRedStarProper h g L1 T1 L2 T2 = (ygt h g L1 T1 L2 T2).
-
-axiom fw_ygt: ∀h,g,L1,L2,T1,T2. ♯{L2, T2} < ♯{L1, T1} → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.
-
-axiom ygt_yprs_trans: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ >[g] ⦃L, T⦄ →
- h ⊢ ⦃L, T⦄ ≥[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ >[g] ⦃L2, T2⦄.