从同一页面中抓取两个HTML表单中的数据

So I've searched through some posts, and I've seen that I can't use a HTML form within another HTML form. Like:

<form method="post" action="x.php">
    <input type="..."/>
    <form method="post" action="x.php">
        <input type="..."/>
    </form>
</form>

Ok, but my problem is that I want to make a different page, which contains HTML code like this:

<?php
if(isset($_GET['vote']) && $_GET['vote']=='yes'){
    echo 'vote successfully inserted';
}

# gets the email value from MAIN form
$email = isset($_POST['email'] : $_POST['email'] : NULL;

#grab the infos from bd for the user with that email,
$stmt = $db->prepare('SELECT name,email,vote FROM tbl WHERE email=:e');
$stmt->execute(array(':e'=>$email));
while($row = $stmt->fetch(PDO::FETCH_OBJ)){
    if($row->vote == 'no'){ # IF THE USER DIDN'T VOTED, THEN
        if(isset($_POST['vote'])){ # IF THE <a> IS PRESSED, UPDATE DB
            $sql = "UPDATE tbl SET vote='yes' WHERE email=:e";
            $s = $db->prepare($sql);
            $s->execute(array(':e'=>$email));
        }
    }
    ?>
    <table>
        <tr>
            <td>Name</td>
            <td>Email</td>
            <td>Address</td>
            <td>Vote</td>
        </tr>
        <tr>
            <td><?php echo $row->name;?></td>
            <td><?php echo $row->email;?></td>
            <td><?php echo $row->address;?></td>
            <td>
                <form method="POST" action="" id="SECOND">
                    <a href="index.php?vote=yes" name="vote">VOTE!</a>
                 </form>
             </td>
        </tr>
    </table>
<?php } // end while() ?>

Then, under this <table>, I have another form:

<form action="" method="POST" id="MAIN>
    <input type="text" name="email" placeholder="email"><br/>
    <input type="submit" value="Login" name="submit"/>
</form>

The project is about a electoral campaign, where a user can 'login' with this email address, and submit his vote. So,

1. when the user requests the page, the MAIN form will pop-up, he will fill in his email, and will press submit.
2. he is redirected to the same page (I'm hiding the MAIN form), and the table will pop-up.
3. now, the user can select his favorite candidate, and press on the <a> link - his vote will be stored in db, updating the vote field from, initially 'no' to 'yes'.

Now, the prob is that when the <a> link is pressed, the update in the db doesn't take place.

The reason the link doesn't update the database is because the form is not being submitted. Change the to an

<input type="submit" value="VOTE!">