theorem
  A* = E^omega implies Lex(E) c= A
proof
  assume
A1: A* = E^omega;
  thus thesis
  proof
    let x be object;
    assume
A2: x in Lex(E);
    then ex e st e in E & x = <%e%> by Def4;
    hence thesis by A1,A2,Th72;
  end;
end;
