- renamed ocaml/ to components/

[helm.git] / helm / matita / library / higher_order_defs / functions.ma

diff --git a/helm/matita/library/higher_order_defs/functions.ma b/helm/matita/library/higher_order_defs/functions.ma
deleted file mode 100644 (file)
index a1b54c8..0000000
--- a/helm/matita/library/higher_order_defs/functions.ma
+++ /dev/null
@@ -1,67 +0,0 @@
-(**************************************************************************)
-(*       ___                                                               *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
-(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU Lesser General Public License Version 2.1         *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/higher_order_defs/functions/".
-
-include "logic/equality.ma".
-
-definition compose \def
-  \lambda A,B,C:Type.\lambda f:(B\to C).\lambda g:(A\to B).\lambda x:A.
-  f (g x).
-
-notation "hvbox(a break \circ b)" 
-  left associative with precedence 70
-for @{ 'compose $a $b }.
-
-interpretation "function composition" 'compose f g =
-  (cic:/matita/higher_order_defs/functions/compose.con _ _ _ f g).
-
-definition injective: \forall A,B:Type.\forall f:A \to B.Prop
-\def \lambda A,B.\lambda f.
-  \forall x,y:A.f x = f y \to x=y.
-
-definition surjective: \forall A,B:Type.\forall f:A \to B.Prop
-\def \lambda A,B.\lambda f.
-  \forall z:B. \exists x:A.z=f x.
-
-definition symmetric: \forall A:Type.\forall f:A \to A\to A.Prop
-\def \lambda A.\lambda f.\forall x,y.f x y = f y x.
-
-definition symmetric2: \forall A,B:Type.\forall f:A \to A\to B.Prop
-\def \lambda A,B.\lambda f.\forall x,y.f x y = f y x.
-
-definition associative: \forall A:Type.\forall f:A \to A\to A.Prop
-\def \lambda A.\lambda f.\forall x,y,z.f (f x y) z = f x (f y z).
-
-theorem eq_f_g_h:
-  \forall A,B,C,D:Type.
-  \forall f:C \to D.\forall g:B \to C.\forall h:A \to B.
-  f \circ (g \circ h) = (f \circ g) \circ h.
-  intros.
-  reflexivity.
-qed.
-
-(* functions and relations *)
-definition monotonic : \forall A:Type.\forall R:A \to A \to Prop.
-\forall f:A \to A.Prop \def
-\lambda A. \lambda R. \lambda f. \forall x,y:A.R x y \to R (f x) (f y).
-
-(* functions and functions *)
-definition distributive: \forall A:Type.\forall f,g:A \to A \to A.Prop
-\def \lambda A.\lambda f,g.\forall x,y,z:A. f x (g y z) = g (f x y) (f x z).
-
-definition distributive2: \forall A,B:Type.\forall f:A \to B \to B.
-\forall g: B\to B\to B. Prop
-\def \lambda A,B.\lambda f,g.\forall x:A.\forall y,z:B. f x (g y z) = g (f x y) (f x z).
-