reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, a1, a2, b for Element of E^omega;
reserve i, k, l, m, n for Nat;

theorem Th35:
  (A |^ m) |^.. n c= A |^.. (m * n)
proof
  let x be object;
  assume x in (A |^ m) |^.. n;
  then consider k such that
A1: k >= n and
A2: x in (A |^ m) |^ k by Th2;
A3: m * k >= m * n by A1,XREAL_1:64;
  x in A |^ (m * k) by A2,FLANG_1:34;
  hence thesis by A3,Th2;
end;
