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Yes, but given that neither process has been attempted yet, I don't think there's any basis to judge correctness. Impeachment has not been initiated by the House. And the 25th never advanced to the stage of delivering a formal Declaration of unfitness to the Speaker and President pro tempore of the Senate. What there seems to have been is some private speach about the 25th among some members of Trump's own Executive Branch. And there's a good amount of pretty public discussion about impeachment.
Neither of those even remotely amount to a "coup" or anything un-Constitutional.
If it had gotten to the stage of formally declaring, then those involved should have been tried for treason.