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 Th7:
  for W be non empty Subset of V holds Maps W c= Maps V
proof
  let W be non empty Subset of V;
  let x be object;
  assume x in Maps W;
  then consider A,B be Element of W, f be Element of Funcs(W) such that
A1: x = [[A,B],f] &( B = {} implies A = {}) & f is Function of A,B;
  Funcs W c= Funcs V & f in Funcs(W) by Th3;
  hence thesis by A1;
end;
