I'm an undergraduate student learning German as the third foreign language. Yesterday I came across Fridericus-Rex-Grenadiermarsch, which contains the following lines:
Die Kais’rin hat sich mit dem Franzosen alliiert,
und das Römische Reich gegen mich revoltiert,
die Russen sind gefallen in Preußen ein,
auf, lasst uns zeigen, dass wir brave Landeskinder sein.
I am perplexed by the last word here. Why "sein," not "sind"? It makes no sense to me. "Sein" is the infinitive form of the German equivalent of "to be" and thus seems to make the whole sentence as absurd as "c'mon, let's show that we be brave sons of our land." I'd put the verb in the third person present plural form - "sind," the German equivalent of "are."
The third line - about the Russians - seems to be against the rules, too. I was taught to always put the participle at the end: "Die Russen sind in Preußen eingefallen." According to what I was taught, this is the only correct way to say, "The Russians have invaded Prussia." Sure, I can move the participle to the beginning, "Eingefallen in Preußen sind die Russen," but I think it will make the whole sentence sound rather as, "Those who invaded Prussia are the Russians." What the author of the song did with the participle seems unthinkable to me. He threw the participle in the middle of the sentence, tearing the prefix off and attaching it at the end of the line.
I cringe to think what my German teacher would do if I wrote my essays like the author of that song. Would be a good illustration of "rotsehen," I guess.
How can such apparent grave grammar mistakes in one of the most known German military marches be explained?