How to check for smaller Uints in Cairo?

Your first option makes more sense.

Uint256 is a hack to implement 256 bits integers that are greater than the max felt.

It is also the option OpenZeppelin chose as shown in their ERC20 implementation of decimals (here for uint8)

You only have to check the range using assert_le every time you set the value of the uint32 or create a special helper function for that.

Initializing the pool is a simple function that accepts two balances for the tokens (A,B), and sets them using the set_pool_token_balance function we defined above: The POOL_UPPER_BOUND is a constant defined to prevent overflows.

Having this function defined, we proceed to add demo tokens to an account: @external func add_demo_token{ syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr, }(token_a_amount: felt, token_b_amount: felt) { let (account_id) = get_caller_address();

// Make sure the account's balance is much smaller than
// the pool init balance.
assert_nn_le(token_a_amount, ACCOUNT_BALANCE_BOUND - 1);
assert_nn_le(token_b_amount, ACCOUNT_BALANCE_BOUND - 1);

modify_account_balance(
    account_id=account_id,
    token_type=TOKEN_TYPE_A,
    amount=token_a_amount,
);
modify_account_balance(
    account_id=account_id,
    token_type=TOKEN_TYPE_B,
    amount=token_b_amount,
);

return ();

}