- new component "s_transition" for the restored fqu and fquq

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / s_transition / fqu.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu.ma b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu.ma
new file mode 100644 (file)
index 0000000..cfc15ca
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+++ b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu.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_2/notation/relations/supterm_6.ma".
+include "basic_2/grammar/lenv.ma".
+include "basic_2/grammar/genv.ma".
+include "basic_2/relocation/lifts.ma".
+
+(* SUPCLOSURE ***************************************************************)
+
+(* activate genv *)
+inductive fqu: tri_relation genv lenv term ≝
+| fqu_lref_O : ∀I,G,L,V. fqu G (L.ⓑ{I}V) (#0) G L V
+| fqu_pair_sn: ∀I,G,L,V,T. fqu G L (②{I}V.T) G L V
+| fqu_bind_dx: ∀p,I,G,L,V,T. fqu G L (ⓑ{p,I}V.T) G (L.ⓑ{I}V) T
+| fqu_flat_dx: ∀I,G,L,V,T. fqu G L (ⓕ{I}V.T) G L T
+| fqu_drop   : ∀I,G,L,V,T,U. ⬆*[1] T ≡ U → fqu G (L.ⓑ{I}V) U G L T
+.
+
+interpretation
+   "structural successor (closure)"
+   'SupTerm G1 L1 T1 G2 L2 T2 = (fqu G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fqu_lref_S: ∀I,G,L,V,i. ⦃G, L.ⓑ{I}V, #(⫯i)⦄ ⊐ ⦃G, L, #(i)⦄.
+/2 width=1 by fqu_drop/ qed.
+
+(* Basic_2A1: removed theorems 3:
+              fqu_drop fqu_drop_lt fqu_lref_S_lt
+*)