theorem
  for A, R, P, P1, P2 st P is (A, R)-correct & P = P1^P2 holds
      P1 is (A, R)-correct
proof
  let A, R, P, P1, P2;
  assume that
    A1: P is (A, R)-correct and
    A2: P = P1^P2;
  set P0 = <*>GRZ-formula-set;
  let k;
  assume A3: k in dom P1;
  dom P1 c= dom P by A2, FINSEQ_1:26;
  then P1^P0, k is_a_correct_step_wrt A, R by A1, A2, A3, Lm41;
  hence P1, k is_a_correct_step_wrt A, R by FINSEQ_1:34;
end;
