lambda finaly moved in lib

[helm.git] / matita / matita / lib / lambda / terms / parallel_computation.ma

diff --git a/matita/matita/lib/lambda/terms/parallel_computation.ma b/matita/matita/lib/lambda/terms/parallel_computation.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 "terms/parallel_reduction.ma".
+
+(* PARALLEL COMPUTATION (MULTISTEP) *****************************************)
+
+definition preds: relation term ≝ star … pred.
+
+interpretation "parallel computation"
+   'ParRedStar M N = (preds M N).
+
+lemma preds_refl: reflexive … preds.
+//
+qed.
+
+lemma preds_step_sn: ∀M1,M. M1 ⤇ M → ∀M2. M ⤇* M2 → M1 ⤇* M2.
+/2 width=3/
+qed-.
+
+lemma preds_step_dx: ∀M1,M. M1 ⤇* M → ∀M2. M ⤇ M2 → M1 ⤇* M2.
+/2 width=3/
+qed-.
+
+lemma preds_step_rc: ∀M1,M2. M1 ⤇ M2 → M1 ⤇* M2.
+/2 width=1/
+qed.
+
+lemma preds_compatible_abst: compatible_abst preds.
+/3 width=1/
+qed.
+
+lemma preds_compatible_sn: compatible_sn preds.
+/3 width=1/
+qed.
+
+lemma preds_compatible_dx: compatible_dx preds.
+/3 width=1/
+qed.
+
+lemma preds_compatible_appl: compatible_appl preds.
+/3 width=1/
+qed.
+
+lemma preds_lift: liftable preds.
+/2 width=1/
+qed.
+
+lemma preds_inv_lift: deliftable_sn preds.
+/3 width=3 by star_deliftable_sn, pred_inv_lift/
+qed-.
+
+lemma preds_dsubst_dx: dsubstable_dx preds.
+/2 width=1/
+qed.
+
+lemma preds_dsubst: dsubstable preds.
+/2 width=1/
+qed.
+
+theorem preds_trans: transitive … preds.
+/2 width=3 by trans_star/
+qed-.
+
+lemma preds_strip: ∀M0,M1. M0 ⤇* M1 → ∀M2. M0 ⤇ M2 →
+                   ∃∃M. M1 ⤇ M & M2 ⤇* M.
+/3 width=3 by star_strip, pred_conf/
+qed-.
+
+theorem preds_conf: confluent … preds.
+/3 width=3 by star_confluent, pred_conf/
+qed-.