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 Th10:
  s -->. t, S implies s ==>. t, S
proof
  assume
A1: s -->. t, S;
  take e = <%>E;
A2: t = {}^t^{}
    .= e^t^e;
  s = {}^s^{}
    .= e^s^e;
  hence thesis by A1,A2;
end;
