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 Th46:
  s in Lang(w, S) iff w ==>* s, S
proof
  thus s in Lang(w, S) implies w ==>* s, S
  proof
    assume s in Lang(w, S);
    then ex t st t = s & w ==>* t, S;
    hence thesis;
  end;
  thus thesis;
end;
