reserve E, x, y, X for set;
reserve A, B, C, D for Subset of E^omega;
reserve a, a1, a2, b, c, c1, c2, d, ab, bc for Element of E^omega;
reserve e for Element of E;
reserve i, j, k, l, n, n1, n2, m for Nat;

theorem Th40:
  a in C |^ m & b in C |^ n implies a ^ b in C |^ (m + n)
proof
  assume a in C |^ m & b in C |^ n;
  then a ^ b in (C |^ m) ^^ (C |^ n) by Def1;
  hence thesis by Th33;
end;
