
theorem Th7:
  for S being continuous complete non empty Poset, A being set st
  A is_FreeGen_set_of S holds A is Subset of S
proof
  set T = the continuous complete non empty Poset;
  let S be continuous complete non empty Poset, A be set such that
A1: A is_FreeGen_set_of S;
  set f = the Function of A, the carrier of T;
  consider h being CLHomomorphism of S, T such that
A2: h|A = f and
  for h9 being CLHomomorphism of S, T st h9|A = f holds h9 = h by A1;
  dom (h|A) = dom h /\ A by RELAT_1:61;
  hence thesis by A2,FUNCT_2:def 1;
end;
