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 Th25:
  A |^ 1 = A
proof
  consider concat being sequence of  bool (E^omega) such that
A1: A |^ 1 = concat.1 and
A2: concat.0 = {<%>E} & for i holds concat.(i + 1) = concat.i ^^ A by Def2;
  thus A |^ 1 = concat.(0 + 1) by A1
    .= {<%>E} ^^ A by A2
    .= A by Th13;
end;
