src/HOL/PreList.thy
author wenzelm
Fri, 15 Dec 2000 17:59:30 +0100
changeset 10680 26e4aecf3207
parent 10671 ac6b3b671198
child 10733 59f82484e000
permissions -rw-r--r--
tuned comment;

(*  Title:      HOL/PreList.thy
    ID:         $Id$
    Author:     Tobias Nipkow
    Copyright   2000 TU Muenchen

A basis for building theory List on. Is defined separately to serve as a
basis for theory ToyList in the documentation.
*)

theory PreList =
  Option + Wellfounded_Relations + NatSimprocs + Recdef + Record +
  Relation_Power + Calculation + SVC_Oracle:

(*belongs to theory HOL*)
declare case_split [cases type: bool]

(*belongs to theory Wellfounded_Recursion*)
declare wf_induct [induct set: wf]

(*belongs to theory Datatype_Universe; hides popular names *)
hide const Node Atom Leaf Numb Lim Funs Split Case


(* generic summation indexed over nat *)

(*FIXME move to Ring_and_Field, when it is made part of main HOL (!?)*)
(*FIXME port theorems from Algebra/abstract/NatSum*)

consts
  Summation :: "(nat => 'a::{zero,plus}) => nat => 'a"
primrec
  "Summation f 0 = 0"
  "Summation f (Suc n) = Summation f n + f n"

syntax
  "_Summation" :: "idt => nat => 'a => nat"    ("\<Sum>_<_. _" [0, 51, 10] 10)
translations
  "\<Sum>i < n. b" == "Summation (\<lambda>i. b) n"

theorem Summation_step:
    "0 < n ==> (\<Sum>i < n. f i) = (\<Sum>i < n - 1. f i) + f (n - 1)"
  by (induct n) simp_all

end