-(**************************************************************************)
-(* ___ *)
-(* ||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/notation/relations/dpconvstar_8.ma".
-include "basic_2/computation/cpds.ma".
-
-(* DECOMPOSED EXTENDED PARALLEL EQUIVALENCE FOR TERMS ***********************)
-
-definition cpes: ∀h. sd h → nat → nat → relation4 genv lenv term term ≝
- λh,g,l1,l2,G,L,T1,T2.
- ∃∃T. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l1] T & ⦃G, L⦄ ⊢ T2 •*➡*[h, g, l2] T.
-
-interpretation "decomposed extended parallel equivalence (term)"
- 'DPConvStar h g l1 l2 G L T1 T2 = (cpes h g l1 l2 G L T1 T2).
-
-(* Basic properties *********************************************************)
-
-lemma cpds_div: ∀h,g,G,L,T1,T2,T,l1,l2.
- ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l1] T → ⦃G, L⦄ ⊢ T2 •*➡*[h, g, l2] T →
- ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2.
-/2 width=3 by ex2_intro/ qed.
-
-lemma cpes_refl_O_O: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l →
- ⦃G, L⦄ ⊢ T •*⬌*[h, g, 0, 0] T.
-/3 width=3 by cpds_refl, cpds_div/ qed.
-
-lemma cpes_sym: ∀h,g,G,L,T1,T2,l1,l2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2 →
- ⦃G, L⦄ ⊢ T2 •*⬌*[h, g, l2, l1] T1.
-#h #g #G #L #T1 #T2 #L1 #l2 * /2 width=3 by cpds_div/
-qed-.