update for the article

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpmre.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/predeval_6.ma".
+include "basic_2/rt_transition/cnr.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* EVALUATION FOR T-BOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION ON TERMS *)
+
+(* Basic_2A1: uses: cprre *)
+definition cpmre (h) (n) (G) (L): relation2 term term ≝
+           λT1,T2. ∧∧ ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃T2⦄.
+
+interpretation "evaluation for t-bound context-sensitive parallel rt-transition (term)"
+   'PRedEval h n G L T1 T2 = (cpmre h n G L T1 T2).
+
+(* Basic properties *********************************************************)
+
+lemma cpmre_intro (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃T2⦄ → ⦃G,L⦄⊢T1➡*[h,n]𝐍⦃T2⦄.
+/2 width=1 by conj/ qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpmre_fwd_cpms (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄⊢T1➡*[h,n]𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2.
+#h #n #G #L #T1 #T2 * //
+qed-.