theorem Th40:
  for A, R for a being Element of A holds <*a*> is (A, R)-correct
proof
  let A, R;
  let a be Element of A;
  set P = <*a*>;
  let k;
  assume k in dom P;
  then P.k in rng P by FUNCT_1:3;
  then P.k in {a} by FINSEQ_1:38;
  then P.k = a by TARSKI:def 1;
  hence <*a*>, k is_a_correct_step_wrt A, R;
end;
