reserve i, j, k, l, m, n for Nat,
  a, b, c, t, u for object,
  X, Y, Z for set,
  D, D1, D2, Fml for non empty set;
reserve p, q, r, s for FinSequence;
 reserve R, R1, R2 for Rule;
 reserve A, A1, A2 for non empty set;
 reserve B, B1, B2 for set;
 reserve P, P1, P2 for Formula-sequence;
 reserve S, S1, S2 for Formula-finset;

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;
