theorem Th14:
  W = {F} implies len(W) = len F
proof
  assume
A1: W = {F};
  then
A2: F in W by TARSKI:def 1;
  now
    assume ex x being object st x in W\{F};
    then consider x such that
A3: x in W\{F};
    x in W by A3,XBOOLE_0:def 5;
    hence contradiction by A1,A3,XBOOLE_0:def 5;
  end;
  then
A4: W\{F}={}H by XBOOLE_0:def 1;
  len(W) = (len(W) - len F) + len F .= len(W\{F}) + len F by A2,Th10
    .= 0 + len F by A4,Th13;
  hence thesis;
end;
