- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / fpn / fpn.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpn/fpn.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpn/fpn.etc
new file mode 100644 (file)
index 0000000..406e6eb
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpn/fpn.etc
@@ -0,0 +1,39 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/btpredsn_8.ma".
+include "basic_2/relocation/lleq.ma".
+include "basic_2/reduction/lpx.ma".
+
+(* REDUCTION FOR "BIG TREE" NORMAL FORMS ************************************)
+
+inductive fpn (h) (g) (G) (L1) (T): relation3 genv lenv term ≝
+| fpn_intro: ∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → L1 ⋕[T] L2 → fpn h g G L1 T G L2 T
+.
+
+interpretation
+   "reduction for 'big tree' normal forms (closure)"
+   'BTPRedSn h g G1 L1 T1 G2 L2 T2 = (fpn h g G1 L1 T1 G2 L2 T2).
+
+(* Basic_properties *********************************************************)
+
+lemma fpn_refl: ∀h,g. tri_reflexive … (fpn h g).
+/2 width=1 by fpn_intro/ qed.
+
+(* Basic inversion lemmas ***************************************************) 
+
+lemma fpn_inv_gen: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊢ ⋕➡[h, g] ⦃G2, L2, T2⦄ →
+                   ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡[h, g] L2 & L1 ⋕[T1] L2 & T1 = T2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and4_intro/
+qed-.