-we would check
The word comprobaríamos is the conditional form of comprobar in the first person plural.
See the full comprobar conjugation


¿No pensó que lo comprobaríamos?
Did you not think we'd check?
Así celebraríamos el primer debate común europeo sobre nuestro futuro en común y comprobaríamos si el federalismo es capaz de frustrar nuestra misión de lograr una Europa de las democracias.
In that way, we should obtain the first common European debate on our common future, and we should be able to see whether federalism could defeat our mission to bring about a Europe of democracies.
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