reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem
  x in X \ A implies chi(A,X).x = 0
proof
  assume
A1: x in X\A;
  then not x in A by XBOOLE_0:def 5;
  hence thesis by A1,Def3;
end;
