theorem
  m <= n & <%>E in A implies (A |^ (m, n))* = (A*) |^ (m, n)
proof
  assume that
A1: m <= n and
A2: <%>E in A;
  (A |^ (m, n))* = (A |^ n)* & A* |^ (m, n) = A* |^ n by A1,A2,Th34,FLANG_1:48;
  hence thesis by A2,Th17;
end;
