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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
(*                                                                          *)
(****************************************************************************)
(*                               Ensf_inter.v                               *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
(*									*)
(*  INTERSECTION 							*)
(*   L'intersection de 2 ensembles est definie comme un predicat sur    *)
(*   3 ensembles A B C en disant que C est l'intresection de A et B     *)
(*   si C est le plus grand ensemble inclus dans A et dans B		*)
(*									*)
Definition inter (A B C : Ensf) : Prop :=
inclus C A /\
inclus C B /\ (forall x : Elt, dans x A -> dans x B -> dans x C).

Lemma union_inter :
forall a b c : Ensf,
inter a b empty -> inter a c empty -> inter a (union b c) empty.