theorem Th43:
  for A, R, S1, S2 st S1 is (A, R)-correct & S2 is (A, R)-correct holds
      S1 \/ S2 is (A, R)-correct
proof
  let A, R, S1, S2;
  assume
    A1: S1 is (A, R)-correct & S2 is (A, R)-correct;
  consider P1, P2 such that
    A3: P1 is (A, R)-correct and
    A4: S1 = rng P1 and
    A5: P2 is (A, R)-correct and
    A6: S2 = rng P2 by A1;
    reconsider S = rng(P1^P2) as GRZ-formula-finset;
    S = S1 \/ S2 by A4, A6, FINSEQ_1:31;
    hence thesis by A3, A5, Th42;
end;
