user6917: I recently edited the Wikipedia article 50 Move Rule as follows:    

The rationale for this rule is that pawn moves and captures are the
  only '''irreversible''' types of moves.  That is, after each pawn move
  or capture, it is impossible for any previous position in the game to
  be repeated.

Unfortunately, my edit was quickly removed with the comment: This is unreferenced. Come up with a reference if you can.
I think this is pretty clear just by thinking about it, but is there any "formal proof" published anywhere that what I tried to add to the article is true?
EDIT: The words "the only" should be deleted.  In addition to captures and pawn moves, losing the right to castle on either or both sides (by moving a rook or king), or failing to capture a certain pawn "en passant" (thus giving up the right to do so later) are also irreversible.  These logically should also reset the 50-move count but are omitted from the rules for reasons of simplicity.

user70: The only 'formal proof' you need is a reference to the rule book of the appropriate governing body. In the US, this could be the USCF.  For international events, it would be FIDE.

user4418: Whoever gave the reason they did for removing your edit was being kind. Your supposed  rationale for the rule is not correct. The 50 move rule and the 3 fold repetition rule are there to cut short games which are going nowhere. 
If there are captures or pawn moves then the nature of the position is changing and there is the possibility of one side or the other winning or losing via these moves. In blocked positions where such moves are either impossible for either side or suicidal it makes no sense to just go on pushing wood. Irreversibility has nothing whatsoever to do with it.

user17646: The two irreversible moves can be proved irreversible (it is impossible to replicate that board state later in the game) like so:
Assumptions:
 - Pawns can't move backward.
 - Every pawn move moves it forward.
 - Pieces can't be added to the board.
 - There is no way to create a pawn (unlike queens, bishops, knights, and rooks which can be created via pawn promotion).
Firstly, captures can be proved irreversible because they always remove a piece from the board. If a board state has N pieces and one is removed you now have N-1 pieces. There is no way to increase the number of pieces so you can never return to N pieces.
Secondly, since every pawn move moves it forward, a pawn can never return to its original position. The only way to have a pawn in that position later on is to have it be occupied by another pawn. But for another pawn to occupy the position that pawn has to move. There is only a finite number of pawns so after every pawn has moved to fill the position left by the previous pawn there are no pawns left to fill the position of the last pawn, preventing the board state from being reached again.

6917: <p>I recently edited the Wikipedia article <a href="https://en.wikipedia.org/wiki/Fifty-move_rule" rel="nofollow">50 Move Rule</a> as follows:    </p>

<blockquote>
  <p>The rationale for this rule is that pawn moves and captures are the
  only '''irreversible''' types of moves.  That is, after each pawn move
  or capture, it is impossible for any previous position in the game to
  be repeated.</p>
</blockquote>

<p>Unfortunately, my edit was quickly removed with the comment: <code>This is unreferenced. Come up with a reference if you can.</code></p>

<p>I think this is pretty clear just by thinking about it, but is there any "formal proof" published anywhere that what I tried to add to the article is true?</p>

<p><strong>EDIT:</strong> The words "the only" should be deleted.  In addition to captures and pawn moves, losing the right to castle on either or both sides (by moving a rook or king), or failing to capture a certain pawn "en passant" (thus giving up the right to do so later) are also irreversible.  These logically should also reset the 50-move count but are omitted from the rules for reasons of simplicity.</p>
 70: <p>The only 'formal proof' you need is a reference to the rule book of the appropriate governing body. In the US, this could be the USCF.  For international events, it would be FIDE.</p>
 4418: <p>Whoever gave the reason they did for removing your edit was being kind. Your supposed  rationale for the rule is not correct. The 50 move rule and the 3 fold repetition rule are there to cut short games which are going nowhere. </p>

<p>If there are captures or pawn moves then the nature of the position is changing and there is the possibility of one side or the other winning or losing via these moves. In blocked positions where such moves are either impossible for either side or suicidal it makes no sense to just go on pushing wood. Irreversibility has nothing whatsoever to do with it.</p>
 17646: <p>The two irreversible moves can be proved irreversible (it is impossible to replicate that board state later in the game) like so:</p>

<p>Assumptions:
 - Pawns can't move backward.
 - Every pawn move moves it forward.
 - Pieces can't be added to the board.
 - There is no way to create a pawn (unlike queens, bishops, knights, and rooks which can be created via pawn promotion).</p>

<p>Firstly, captures can be proved irreversible because they always remove a piece from the board. If a board state has N pieces and one is removed you now have N-1 pieces. There is no way to increase the number of pieces so you can never return to N pieces.</p>

<p>Secondly, since every pawn move moves it forward, a pawn can never return to its original position. The only way to have a pawn in that position later on is to have it be occupied by another pawn. But for another pawn to occupy the position <em>that</em> pawn has to move. There is only a finite number of pawns so after every pawn has moved to fill the position left by the previous pawn there are no pawns left to fill the position of the last pawn, preventing the board state from being reached again.</p>
