reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

theorem Th83:
  A c= [:X,Y:] & z in A implies
    ex x,y st x in X & y in Y & z = [ x,y]
proof
  assume A c= [:X,Y:] & z in A;
  then z in [:X,Y:];
  hence thesis by Def2;
end;
