reserve i, j, k, l, m, n, t for Nat;

theorem
  n > 0 implies 2 to_power n mod 2 = 0
proof
  assume n > 0;
  then
A1: n >= 0 + 1 by NAT_1:13;
  2 to_power n = 2 to_power (n - 1 + 1)
    .= 2 to_power (n-'1 + 1) by A1,XREAL_1:233
    .= 2 to_power (n-'1) * (2 to_power 1) by POWER:27
    .= 2 to_power (n-'1) * 2 by POWER:25;
  hence thesis by NAT_D:13;
end;
