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Rd5
1. Q G3+
2. K x E4
3. Q E3 #
1.Rd5+ Kxe4
2.Qg2+ Kf4
3.Qg3+ Ke4
4.Re5#
I can’t say for certain right now that white can’t still mate black, Andreas, but your line overlooks 3. …Kf5. But don’t feel bad, I had my eyes on this exact line, too.