reserve x for set;
reserve k, l for Nat;
reserve p, q for FinSequence;
reserve R for Relation;
reserve p, q for RedSequence of R;
reserve E for set;
reserve s, t for XFinSequence;
reserve p, q for XFinSequence-yielding FinSequence;
reserve E for set;
reserve S, T, U for semi-Thue-system of E;
reserve s, t, s1, t1, u, v, u1, v1, w for Element of E^omega;
reserve p for FinSequence of E^omega;

theorem Th33:
  s ==>. t, S implies s ==>* t, S
proof
  assume s ==>. t, S;
  then [s, t] in ==>.-relation(S) by Def6;
  then ==>.-relation(S) reduces s, t by REWRITE1:15;
  hence thesis;
end;
