- renamed ocaml/ to components/

[helm.git] / helm / matita / library / list / list.ma

diff --git a/helm/matita/library/list/list.ma b/helm/matita/library/list/list.ma
deleted file mode 100644 (file)
index ffa2c8e..0000000
--- a/helm/matita/library/list/list.ma
+++ /dev/null
@@ -1,112 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/list/".
-include "logic/equality.ma".
-include "higher_order_defs/functions.ma".
-
-inductive list (A:Set) : Set :=
-  | nil: list A
-  | cons: A -> list A -> list A.
-
-notation "hvbox(hd break :: tl)"
-  right associative with precedence 46
-  for @{'cons $hd $tl}.
-
-notation "[ list0 x sep ; ]"
-  non associative with precedence 90
-  for ${fold right @'nil rec acc @{'cons $x $acc}}.
-
-notation "hvbox(l1 break @ l2)"
-  right associative with precedence 47
-  for @{'append $l1 $l2 }.
-
-interpretation "nil" 'nil = (cic:/matita/list/list.ind#xpointer(1/1/1) _).
-interpretation "cons" 'cons hd tl =
-  (cic:/matita/list/list.ind#xpointer(1/1/2) _ hd tl).
-
-(* theorem test_notation: [O; S O; S (S O)] = O :: S O :: S (S O) :: []. *)
-
-theorem nil_cons:
-  \forall A:Set.\forall l:list A.\forall a:A.
-    a::l <> [].
-  intros;
-  unfold Not;
-  intros;
-  discriminate H.
-qed.
-
-let rec id_list A (l: list A) on l :=
-  match l with
-  [ nil => []
-  | (cons hd tl) => hd :: id_list A tl ].
-
-let rec append A (l1: list A) l2 on l1 :=
-  match l1 with
-  [ nil => l2
-  | (cons hd tl) => hd :: append A tl l2 ].
-
-definition tail := \lambda A:Set. \lambda l: list A.
-  match l with
-  [ nil => []
-  | (cons hd tl) => tl].
-
-interpretation "append" 'append l1 l2 = (cic:/matita/list/append.con _ l1 l2).
-
-theorem append_nil: \forall A:Set.\forall l:list A.l @ [] = l.
-  intros;
-  elim l;
-  [ reflexivity;
-  | simplify;
-    rewrite > H;
-    reflexivity;
-  ]
-qed.
-
-theorem associative_append: \forall A:Set.associative (list A) (append A).
-  intros; unfold; intros;
-  elim x;
-  [ simplify;
-    reflexivity;
-  | simplify;
-    rewrite > H;
-    reflexivity;
-  ]
-qed.
-
-theorem cons_append_commute:
-  \forall A:Set.\forall l1,l2:list A.\forall a:A.
-    a :: (l1 @ l2) = (a :: l1) @ l2.
-  intros;
-  reflexivity;
-qed.
-
-(*
-theorem nil_append_nil_both:
-  \forall A:Set.\forall l1,l2:list A.
-    l1 @ l2 = [] \to l1 = [] \land l2 = [].
-*)
-
-(*
-include "nat/nat.ma".
-
-theorem test_notation: [O; S O; S (S O)] = O :: S O :: S (S O) :: []. 
-reflexivity.
-qed.
-
-theorem test_append: [O;O;O;O;O;O] = [O;O;O] @ [O;O] @ [O].
-simplify.
-reflexivity.
-qed.
-*)