 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem Counter0:
  for Z being Subset of REAL st not 0 in Z holds
    (id Z)"{0} = {}
  proof
    let Z be Subset of REAL;
    assume
AA: not 0 in Z;
    (id Z)"{0} c= {}
    proof
      let x be object;
      assume x in (id Z)"{0}; then
A2:   x in dom id Z & (id Z).x in {0} by FUNCT_1:def 7; then
      (id Z).x = x by FUNCT_1:17;
      hence thesis by A2,AA,TARSKI:def 1;
    end;
    hence thesis;
  end;
