In English we sometimes combine verbs with auxiliary verbs. Would've = Would have Should've = Should have Your two sentences in English would be one rather than two and read "the party yesterday was great, you would've loved it", since "you would've loved it" is a dependent clause and relies upon "the party yesterday was great" being said to provide context. By adding the "you would've loved it" though, what the person is essentially saying is, "if you were there, you would have loved it".