- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / term_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/term_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/term_vector.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 "ground_2/lib/list.ma".
+include "basic_2/notation/functions/snapplvector_2.ma".
+include "basic_2/syntax/term_simple.ma".
+
+(* TERMS ********************************************************************)
+
+rec definition applv Vs T on Vs ≝
+  match Vs with
+  [ nil        ⇒ T
+  | cons hd tl ⇒ ⓐhd. (applv tl T)
+  ].
+
+interpretation "application to vector (term)"
+   'SnApplVector Vs T = (applv Vs T).
+
+(* Basic properties *********************************************************)
+
+lemma applv_nil: ∀T. Ⓐ◊.T = T.
+// qed.
+
+lemma applv_cons: ∀V,Vs,T. ⒶV@Vs.T = ⓐV.ⒶVs.T.
+// qed.
+
+(* Properties with simple terms *********************************************)
+
+lemma applv_simple: ∀T,Vs. 𝐒⦃T⦄ → 𝐒⦃ⒶVs.T⦄.
+#T * //
+qed.