helm/software/matita/nlibrary/nat/big_ops.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "nat/order.ma".
  16 include "algebra/magmas.ma".
  17
  18 alias symbol "eq" = "leibnitz's equality".
  19 alias id "refl" = "cic:/matita/ng/logic/equality/eq.con(0,1,2)".
  20 nlet rec big_op (M: magma_type) (n: nat) (f: ∀m. lt m n → M) (v: M) on n : M ≝
  21  (match n return λx.∀p:n=x.? with
  22    [ O ⇒ λ_.v
  23    | S n' ⇒ λp.op ? (f n' ?) (big_op M n' ? v) ]) (refl ? n).
  24 ##[ nrewrite > p; napply le_n
  25   | #m; #H; napply (f m); nrewrite > p; napply le_S; nassumption]
  26 nqed.