every premoves are not can always be made safely except - opponent every possible move lead to position when I have only one possible move.
Math problem regarding premoves
well if your pawn is just past the center square for enpassant, say the enemy pawn moves forward two squares to attach a couple knight, and you had some pieces two squares away from said pawn that will be captured by an opposing piece that can't attack diagonally like knight or rook or something, and the enemy king was directly in front of your pawn and precisely two spaces in front of your pawn, and finally your pawn is backed so his king can't capture it when you check him using enpassant, you could capture the rook that captured your piece and it'd be safe to premove after he moves his pawn forward two spaces absolutely.
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Define a subset of premoves consisting of moving your pawn or piece to a square that is already occupied by some other pawn or piece that is also your own. Typical examples of these premoves are recaptures (if the opponent captures your piece or pawn, you capture back).
Prove or disprove : Such kinds of premoves can always be made safely.
By safely, I mean that either the premove fails because the move is illegal or you indeed capture a pawn or piece otherwise.