AS3 - Error 1119 - Does not detect my static class altogether - actionscript-3

Question

Context: I began learning AS3 a week ago. All my files are in the same folder, and the path is set to . (by default anyway), so all classes should logically detect each other. But as it turns out, I have a class with a lot of public static var, and every time I call these in my other class, I get Error 1119
Access of possibly undefined property isKeyJump through a reference with static type Function.
The class with static variables is called Cont for 'Control'; it's basically meant to check which keys are pressed, just pressed, or pressed twice rapidly. I made the class to organize the code, essentially.
I declare all my variables like this:
public static var isKeyRight:Boolean = false;
And if that wasn't sufficiently explicit, I even wrote this in the constructor (I was tired):
public function Cont()
{
Cont.isKeyRight = false;
... }
But that didn't solve the issue at all. It appears the problem is independent from the class itself; it's just that my other class does not detect Cont.
I tried import Cont; but that also didn't change a thing. My 44 lines of Error 1119 look like this:
if (standing && Cont.isKeyJump) vacc = _jumpAcc;
I even made sure to instantiate the instance of Cont before that of my other class, to make sure that the definitions were at least there. But that would probably make an error after compilation if that was the issue, not during.
The bulk:
Other Class: (The one with 44 errors)
package {
import flash.display.MovieClip;
import flash.events.Event;
public class PersonnagePrincipal extends Physical {
//INITIALISATION
...
//CONSTRUCTOR
public function PersonnagePrincipal(life:Number = 100, focus:Number = 100, lifeMax:Number = 100, focusMax:Number = 100)
{
super();
...
}
// GET & SET
public function set life(life:Number):void { _life = (life > lifeMax) ? lifeMax : life; }
...
// UPDATE
override public function update(event:Event)
{
move_physical();
if (standing && Cont.isKeyJump) vacc = _jumpAcc;
...
And Cont:
package {
import flash.events.Event;
import flash.events.KeyboardEvent;
import flash.ui.Keyboard;
import flash.display.MovieClip;
import flash.utils.*;
public class Cont extends MovieClip
{
// Key codes
public static var isKeyRight:Boolean;
public static var isKeyJump:Boolean;
...
//CONSTRUCTOR
public function Cont()
{
Cont.isKeyRight = false;
Cont.isKeyJump = false;
...
if (stage) { init(); }
else { this.addEventListener(Event.ADDED_TO_STAGE, init); }
}
//POST-CONSTRUCTOR
private function init(e:Event=null)
{
this.removeEventListener(Event.ADDED_TO_STAGE, init);
...
}
EDIT: Well, taking all the code from Cont and into PersonnagePrincipal does solve the synthax errors (given that I get rid of the Cont.) ... But now my code is a lot less sexy and flexible.
EDIT 2: I made the class PersonnagePrincipal empty, and it worked. Stranger still, when I put the line public var control:Cont = new Control in Main, it works, while it generates a compile time error in PersonnagePrincipal. What?