update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / computation / fsb.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/computation/fsb.ma b/matita/matita/contribs/lambdadelta/basic_2A/computation/fsb.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_2A/notation/relations/btsn_5.ma".
+include "basic_2A/reduction/fpb.ma".
+include "basic_2A/computation/csx.ma".
+
+(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
+
+inductive fsb (h) (g): relation3 genv lenv term ≝
+| fsb_intro: ∀G1,L1,T1. (
+                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → fsb h g G2 L2 T2
+             ) → fsb h g G1 L1 T1
+.
+
+interpretation
+   "'qrst' strong normalization (closure)"
+   'BTSN h g G L T = (fsb h g G L T).
+
+(* Basic eliminators ********************************************************)
+
+lemma fsb_ind_alt: ∀h,g. ∀R: relation3 …. (
+                      ∀G1,L1,T1. ⦥[h,g] ⦃G1, L1, T1⦄ → (
+                         ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2
+                      ) → R G1 L1 T1
+                   ) →
+                   ∀G,L,T. ⦥[h, g] ⦃G, L, T⦄ → R G L T.
+#h #g #R #IH #G #L #T #H elim H -G -L -T
+/4 width=1 by fsb_intro/
+qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma fsb_inv_csx: ∀h,g,G,L,T. ⦥[h, g] ⦃G, L, T⦄ → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+#h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpb_cpx/
+qed-.