reserve x, X, Y for set;

theorem
  for S being non empty 1-sorted for f being Function of S, S holds f is
  idempotent implies for x being Element of S holds f.(f.x) = f.x
proof
  let L be non empty 1-sorted, p be Function of L,L;
  assume
A1: p*p = p;
  let l be Element of L;
  thus thesis by A1,FUNCT_2:15;
end;
