That was fun and thank you. The formalities of puzzles are that if you say "White to play and mate in 4" that means that regardless of what black does, even moves that lose material without purpose, the mate is in 4 moves. Here, black has 2 stalling moves Rg1+ and then Rb1+ losing his rook. So, again formally, it is a mate in 6 puzzle. Your "white to play and win in 4" is a little less specific and may mean that white just has a winning advantage after 4 moves.
At any rate, good fun puzzle and I must ask if you made it up?
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