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How can white win after 55. BF2?

After 55... Bf2 56. e8=Q and eventually taking the g6 pawn, you can check the position in the tablebase (book icon). It says white wins, and you can click on the moves to see how. It doesn't seem to be so easy though, and I am sure I wouldn't have won that position with white.
@dz123 Nah, once you have the concept, the process is simple. If not in time trouble, the concept is not difficult to figure out. I thought I'd try playing it against an engine, but I'm pretty sure engine won't keep the bishop standing on f2, so there's no way for me to actually "prove" it. Unless someone's willing to play this position out with me.

Here. Like I said, the bishop doesn't stay on f2, but if it did, doesn't matter.
Probably yes, the king marches to c1 and secures the promotion square. Black bishop holds both pawns from c3.
UPD On second thought... god only knows. White king is stalemated, so... probably not, lol.
How is black supposed to win, white just sacs pawns and the bishop against b pawn. Stalemate.
White still wins. White gives Ba2 for Qb1. Then the two white pawns are out of the range of the black king and the bishop cannot hold off both pawns.
Another fun fact:

If white loses on time in this position ...



... black will get granted the win by Lichess though there is no way for white to win :-)

Edit: Same when black loses on time.

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