matita/matita/contribs/lambdadelta/basic_2/syntax/term_vector.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground_2/lib/list.ma".
  16 include "basic_2/notation/functions/snapplvector_2.ma".
  17 include "basic_2/syntax/term_simple.ma".
  18
  19 (* TERMS ********************************************************************)
  20
  21 rec definition applv Vs T on Vs ≝
  22   match Vs with
  23   [ nil        ⇒ T
  24   | cons hd tl ⇒ ⓐhd. (applv tl T)
  25   ].
  26
  27 interpretation "application to vector (term)"
  28    'SnApplVector Vs T = (applv Vs T).
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma applv_nil: ∀T. ⒶⒺ.T = T.
  33 // qed.
  34
  35 lemma applv_cons: ∀V,Vs,T. ⒶV⨮Vs.T = ⓐV.ⒶVs.T.
  36 // qed.
  37
  38 (* Properties with simple terms *********************************************)
  39
  40 lemma applv_simple: ∀T,Vs. 𝐒⦃T⦄ → 𝐒⦃ⒶVs.T⦄.
  41 #T * //
  42 qed.