reserve k,m,n for Nat,
  a, b, c for object,
  x, y, X, Y, Z for set,
  D for non empty set;
reserve p, q, r, s, t, u, v for FinSequence;
reserve P, Q, R, P1, P2, Q1, Q2, R1, R2 for FinSequence-membered set;
reserve S, T for non empty FinSequence-membered set;

theorem Th13:
  for P, Q, R st P c= R* & Q c= R* holds P^Q c= R*
proof
  let P, Q, R;
  assume that A1: P c= R* and A2: Q c= R*;
  let a;
  assume a in P^Q;
  then consider p, q such that A3: a = p^q and A4: p in P and A5: q in Q
      by Def2;
  thus thesis by A1, A2, A3, A4, A5, Th12;
end;
