Hinged lever held by a string - Problem regarding forces

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    Forces Lever String
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[PLAIN]http://img20.imageshack.us/img20/7673/lever.gif

I've come upon this phenomenon that as you shift the load left, or right, or anywhere along the lever, the intersection of the directions for the contact force due to the wall and the tension from the string will always be directly above the center of the load. I figured this out by accurate drawing.

However, is this always true? If Yes, how do you prove it? (i.e., formulas? theories? rules?)
 
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Yes, it's always true. There's a theorem in mechanics that says if three forces act on a body that is in static equilibrium, the lines of action of those three forces must intersect at a single point (or all be parallel). In your example, the weight of the load acts as one of those forces and its line of action is vertical. (I don't know if this theorem has a name--somebody must have been the first to notice it.)
 
If it were not so, there would be a resultant couple and 'something' would rotate. I think that the old system of Bow's (spelling) Notation was based on this fact. We did it a A level, I remember, and it was used for working out the forces in complicated, loaded frameworks in our 'statics' course.