lambda finaly moved in lib

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

diff --git a/matita/matita/lib/lambda/terms/labeled_sequential_computation.ma b/matita/matita/lib/lambda/terms/labeled_sequential_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/sequential_computation.ma".
+
+(* ABSTRACT LABELED SEQUENTIAL COMPUTATION (MULTISTEP) **********************)
+
+definition l_sreds: ∀S. (S→relation term) → list S → relation term ≝
+                    λS,R. lstar … R.
+
+lemma sreds_l_sreds: ∀S,R. (∀M,N. M ↦ N → ∃a. R a M N) →
+                     ∀M,N. M ↦* N → ∃l. l_sreds S R l M N.
+#S #R #HR #M #N #H elim H -N
+[ #N #N0 #_ #HN0 * #l #HMN
+  elim (HR … HN0) -HR -HN0 /3 width=5/
+| /2 width=2/
+]
+qed-.
+
+lemma l_sreds_inv_sreds: ∀S,R. (∀a,M,N. R a M N → M ↦ N) →
+                         ∀l,M,N. l_sreds S R l M N → M ↦* N.
+#S #R #HR #l #M #N #H elim H -N // /3 by star_compl/
+qed-.
+
+(* Note: "|s|" should be unparetesized *)
+lemma l_sreds_fwd_mult: ∀S,R. (∀a,M,N. R a M N → M ↦ N) →
+                        ∀l,M1,M2. l_sreds S R l M1 M2 →
+                        ♯{M2} ≤ ♯{M1} ^ (2 ^ (|l|)).
+#S #R #HR #l #M1 #M2 #H @(lstar_ind_l … l M1 H) -l -M1 normalize //
+#a #l #M1 #M #HM1 #_ #IHM2
+lapply (HR … HM1) -HR -a #HM1
+lapply (sred_fwd_mult … HM1) #HM1
+@(transitive_le … IHM2) -M2
+/3 width=1 by le_exp1, lt_O_exp, lt_to_le/ (**) (* auto: slow without trace *)
+qed-.