reserve x, y, X for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u1, v, v1, v2, w, w9, w1, w2 for Element of E^omega;
reserve F for Subset of E^omega;
reserve i, k, l for Nat;
reserve TS for non empty transition-system over F;
reserve S, T for Subset of TS;

theorem Th9:
  u in Lex(E) iff len u = 1
proof
  thus u in Lex(E) implies len u = 1
  proof
    assume u in Lex(E);
    then ex e st e in E & u = <%e%> by FLANG_1:def 4;
    hence thesis by AFINSQ_1:def 4;
  end;
  assume len u = 1;
  then ex e st <%e%> = u & e = u.0 by Th4;
  hence thesis by FLANG_1:def 4;
end;
