commit is now complete :)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc.ma
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+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc.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/lazybtpredproper_8.ma".
+include "basic_2/computation/fpns.ma".
+include "basic_2/computation/fpbu.ma".
+
+(* SINGLE-STEP "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********)
+
+definition fpbc: ∀h. sd h → tri_relation genv lenv term ≝
+                 λh,g,G1,L1,T1,G2,L2,T2.
+                 ∃∃G,L,T.  ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ .
+
+interpretation
+   "single-step 'big tree' proper parallel reduction (closure)"
+   'LazyBTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbc h g G1 L1 T1 G2 L2 T2).
+
+(* Baic properties **********************************************************)
+
+lemma fpbu_fpbc: ∀h,g,G1,G2,L1,L2,T1,T2.
+                 ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄.
+/2 width=5 by ex2_3_intro/ qed.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc_fpns.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc_fpns.ma
new file mode 100644 (file)
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--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc_fpns.ma
@@ -0,0 +1,34 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/fpns_fpns.ma".
+include "basic_2/computation/fpbu_fpns.ma".
+include "basic_2/computation/fpbc.ma".
+
+(* SINGLE-STEP "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********)
+
+(* Properties on parallel computation for "big tree" normal forms ***********)
+
+lemma fpbc_fpns_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G, L, T⦄ →
+                       ⦃G, L, T⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
+/3 width=9 by fpns_trans, ex2_3_intro/
+qed-.
+
+lemma fpns_fpbc_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G, L, T⦄ →
+                       ⦃G, L, T⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 *
+#G0 #L0 #T0 #H0 #H02 elim (fpns_fpbu_trans … H1 … H0) -G -L -T
+/3 width=9 by fpns_trans, ex2_3_intro/
+qed-.