X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2A%2Freduction%2Ffpbq.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2A%2Freduction%2Ffpbq.ma;h=e1d0d39dca4043d9f1986c217dd930d4addfa0db;hb=d2545ffd201b1aa49887313791386add78fa8603;hp=0000000000000000000000000000000000000000;hpb=57ae1762497a5f3ea75740e2908e04adb8642cc2;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/reduction/fpbq.ma b/matita/matita/contribs/lambdadelta/basic_2A/reduction/fpbq.ma
new file mode 100644
index 000000000..e1d0d39dc
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/reduction/fpbq.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/btpred_8.ma".
+include "basic_2A/substitution/fquq.ma".
+include "basic_2A/multiple/lleq.ma".
+include "basic_2A/reduction/lpx.ma".
+
+(* "QRST" PARALLEL REDUCTION FOR CLOSURES ***********************************)
+
+inductive fpbq (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
+| fpbq_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h g G1 L1 T1 G2 L2 T2
+| fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → fpbq h g G1 L1 T1 G1 L1 T2
+| fpbq_lpx : ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g] L2 → fpbq h g G1 L1 T1 G1 L2 T1
+| fpbq_lleq: ∀L2. L1 ≡[T1, 0] L2 → fpbq h g G1 L1 T1 G1 L2 T1
+.
+
+interpretation
+   "'qrst' parallel reduction (closure)"
+   'BTPRed h g G1 L1 T1 G2 L2 T2 = (fpbq h g G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fpbq_refl: ∀h,g. tri_reflexive … (fpbq h g).
+/2 width=1 by fpbq_cpx/ qed.
+
+lemma cpr_fpbq: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L, T1⦄ ≽[h, g] ⦃G, L, T2⦄. 
+/3 width=1 by fpbq_cpx, cpr_cpx/ qed.
+
+lemma lpr_fpbq: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1, T⦄ ≽[h, g] ⦃G, L2, T⦄.
+/3 width=1 by fpbq_lpx, lpr_lpx/ qed.