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 Th16:
  S is Thue-system of E & s -->. t, S implies t -->. s, S
proof
  assume S is Thue-system of E & s -->. t, S;
  then S = S~ & [s, t] in S by RELAT_2:13;
  then [t, s] in S by RELAT_1:def 7;
  hence thesis;
end;
