I believe that the explanation (this one is difficult to explain) for this is that certain constructions like this - for example: "No sooner had X arrived/sat down/gotten up/etc. " or "No sooner was X settled in/rested/etc. " or "No sooner did X arrive/settle in/etc.
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Tamara Grobschmidt"No sooner had he arrived than she left the party."When a negative or restrictive word or phrase such as no sooner, never, seldom, only, nor, hardly, neither, not until, rarely, scarcely is placed in initial position for emphasis, inversion normally occurs in the main clause. Except for ne