theorem Th5:
  not F in W implies len(L,W \ {F}) = len(L,W)
proof
  assume
A1: not F in W;
A2: for x being object holds x in W implies x in W \ {F}
  proof let x be object;
    assume
A3: x in W;
    then not x in {F} by A1,TARSKI:def 1;
    hence thesis by A3,XBOOLE_0:def 5;
  end;
  for x being object holds x in W \ {F} implies x in W by XBOOLE_0:def 5;
  hence thesis by A2,TARSKI:2;
end;
