Checked : sélectionner checkall - impossible

<?php
$mail = $_POST['mail'];
// Pour n'afficher que les champs remplis , recherche si il y a des champs vide .
$rsql="SELECT ";
for($i=1;$i<=$mail;$i++)
{
  if($i>1) $rsql = $rsql.",";
$rsql = $rsql."if(c$i,'','c$i est vide')";
}
$rsql="FROM `clients` ORDER BY mail != '' DESC";

// ACCES A LA BASE DE DONNEE
include "config.php";

//REQUETE SUR LA TABLE PROPRIOS
$sql_query = "SELECT * FROM

    `clients` ORDER BY mail DESC";

    //$sql_query = 'SELECT * FROM `clients` ORDER BY mail DESC LIMIT '.$limite.','.$nombre.'';
$result = mysql_query($sql_query);
if (!$result) {
	   echo 'Impossible d\'exécuter la requête : ' . mysql_error();
	      exit;
}

// form: crée ou pas le checked sur les champs radios et checkbox
function form_check($mail,$value){
//$checked = ' checked="checked"';
$checked = ' checked=""';
if(isset($_POST[$mail]) && $_POST[$mail]===$value){
return $checked;
}else{
return false;
}
}

// AFFICHAGE PAGE PAR PAGE DES RESULTAT
$nombre = 20;  // on va afficher 5 résultats par page.
if (!isset($limite)) $limite = 0; // si on arrive sur la page pour la première fois
               // on met limite à 0.

$path_parts = pathinfo($_SERVER['PHP_SELF']);
$page = $path_parts['basename'];


echo    "<form name='email' method='post' action='envoimail.php?clients=".$mail."' />";
echo    "<table align='center' class='liste'>";
           echo "<div id=\"div_chck\">";
	       echo "<tr>";
			   	//echo "<td> Tous <input type=checkbox name='$mail' onClick='javascript:document.gestfiles.submit()' value='Cocher'></td>";
                //echo "<td> Tous <input type='checkbox' name='allselect' onClick=\"ManagementCheckBox('')\"  value='Cocher'></td>";

                echo "<td><input type=\"checkbox\" name=\"checkState\" onClick=\"checkState('')\" value=\"checkbox\"($case== true)?\" \" />Tous</td>";
                echo "<td>Soci&eacute;t&eacute;e</td>";
                echo "<td>Civilit&eacute;</td>";
                echo "<td>Nom</td>";
                echo "<td>Pr&eacute;nom</td>";
                echo "<td>Adresse</td>";
                echo "<td>CP</td>";
	       		echo "<td>Ville</td>";
	       		echo "<td>Tel</td>";
                echo "<td>Fax</td>";
                echo "<td>Portable</td>";
	       		echo "<td>Mail</td>";
	       echo "</tr>";

while($row=mysql_fetch_array($result)) {
	       $id= $row['ID'];
           $intitule= $row['intitule'];
           $civilite= $row['civilite'];
           $nom = $row['nom'];
           $prenom = $row['prenom'];
	       $adresse= $row['adresse'];
	       $cp = $row['CP'];
	       $ville= $row['Ville'];
           $tel = $row['Tel'];
           $fax = $row['Fax'];
           $port = $row['portable'];
	       $mail = $row['mail'];


 // pour un bouton checkbox
                echo "<tr>";
                $checked = $value['mail']=1 ? "checked='checked'": "";
                //echo '<input name="email" type="checkbox" value="$mail" ' . $checked .'>';
                //echo '<input name="option1" type="checkbox" value="$mail" '.form_check('option1','mail').' /> ',"\r\n";
                //echo "<td><div id='checkState' align='center' ><input type='checkbox' name='$mail[]' id='checkState' value='".$mail."' onClick='checkState('');' /></div></td>";
                echo "<td><div id='email' align='center' ><input name='mail' type='checkbox' value='$mail' $checked></div></td>";
                //echo "<td align='center' ><input type='checkbox' name=".$proprio_mail['prop_mail']." value=".$proprio_mail['prop_mail']." onClick='checkState()' /></td>";
                echo "<td>" . $intitule ."</td>";
                echo "<td>" . $civilite ."</td>";
	       		echo "<td>" . $nom ."</td>";
 	       		echo "<td>" . $prenom ."</td>";
 	       		echo "<td>" . $adresse ."</td>";
                echo "<td>" . $cp ."</td>";
                echo "<td>" . $ville ."</td>";
                echo "<td>" . $tel ."</td>";
                echo "<td>" . $fax ."</td>";
                echo "<td>" . $port ."</td>";
                echo "<td>" . $mail ."</td>";
    			echo "</td>";
                echo "</tr>";
}
   echo " </div>";
echo "</table>";
echo    ' <div align="center" > <input align="center" name="" type="submit" class="nav" id="envoyer" value="Envoyer" /></div>';

echo    " </form>";
mysql_close($sqllink);
?>

// form: crée ou pas le checked sur les champs radios et checkbox
function form_check($mail,$value){
//$checked = ' checked="checked"';
$checked = ' checked="[color=blue]true[/color]"';
if(isset($_POST[$mail]) && $_POST[$mail]===$value){
return $checked;
}else{
return false;
}
}

echo "<td><input type=\"checkbox\" name=\"checkState\" onClick=\"checkState('')\" value=\"checkbox\"($case== true)?\" \" />[b]TOUS[/b]</td>";

echo "<td><div id='email' align='center' ><input name='checkState' type='checkbox' value='$mail' $checked></div></td>";

echo "<td><input type=\"checkbox\" name=\"checkState\" onClick=\"checkState('')\" value=\"checkbox\"($case== true)?\" \" />[b]TOUS[/b]</td>";

$checked = $value['checkState']=0 ? "checked='checked'": "";
echo '<td align="center" ><input name="email" type="checkbox" value="checkState" '.form_check('email','mail').' /></td>';