Missed Mate/Puzzle

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Here was another win that I managed to convert into a draw with some clueless late middlegame play. The end position was semi-interesting, or at least confusing, and my opponent and I received a little help from some stronger players. After playing Rf4+, the winning move, I offered a draw, unable to see a mate. See the diagram below for the nifty conclusion I missed. 





Middle aged patzer and dad, just trying to improve. All criticism, input, advice and insults welcome.