Der Traum ist dann deiner, dein einer, alleine, den keiner vorher geträumt. Der Traum is the subject, in the nominative case, while deiner is a Prädikativ, a "nominative object". You can tell that from the use of ist (sein), the copula. The part dein einer is a repetition of that deiner, in a slightly different phrasing. It's there for emphasis and clarification.
What is the meaning of "Einer" in this context and how to use it
Understanding usage of eine/einer/.. to mean "one of the" but in ...
Eigentlich dachte ich, ich wüsste es, aber je länger ich schaue und analysiere, desto unsicherer werde ich: Zuerst hieß es "Ich befinde mich in einer Art professionellem Arbeitsverhältnis.&quo...
Technically, yes, der eine can be replaced with einer here, although, as you expected, the meaning would change. The usage of einer is much like one in English and also der eine can be thought of as the one. It shifts the meaning from being any one of a certain group to a certain one from a certain group. In this context, the der is justified: The one behind him brushed against Karl's back ...
Bei einer Antwort auf "Sprechen wir von 4-Taktern; wie gut war der W201?"/"Der W201 war einer der Besten von Mercedes." geht dann, ohne "4-Takter" zu wiederholen.
Why isn't it "eines/eins meines LieblingsLieder" and "eine meine Lieblingsband" instead of "einer meiner" being used with both noun phrases as shown by DeepL and Google Translate? Also, why isn't it "Lieblingsbände" instead of "Lieblingsbands" since die Bände is the plural form of "die Band"?
Why is it "einer meiner" twice and not "eins/eines" and "eine meine ...