reserve V for non empty set,
  A,B,A9,B9 for Element of V;
reserve f,f9 for Element of Funcs(V);
reserve m,m1,m2,m3,m9 for Element of Maps V;

theorem
  Maps V c= [:[:V,V:],Funcs V:]
proof
  let m be object;
  assume m in Maps V;
  then ex A,B,f st m = [[A,B],f] & (B={} implies A={}) & f is Function of A,B;
  hence thesis;
end;
