reserve k,m,n for Element of NAT,
  i, j for Nat,
  a, b, c for object,
  X, Y, Z for set,
  D, D1, D2 for non empty set;
reserve p, q, r, s for FinSequence;
reserve t, u, v, w for GRZ-formula;
reserve R, R1, R2 for GRZ-rule;
reserve A, A1, A2 for non empty Subset of GRZ-formula-set;
reserve B, B1, B2 for Subset of GRZ-formula-set;
reserve P, P1, P2 for GRZ-formula-sequence;
reserve S, S1, S2 for GRZ-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;
