And yet in the introductory classes teachers heavily insisted that "obvious","evident","trivial" shouldn't be part of your vocabulary (you would lose points) an

And yet in the introductory classes teachers heavily insisted that "obvious","evident","trivial" shouldn't be part of your vocabulary (you would lose points) and when using a shortcut you should always reference it... until you got several levels above it (you wouldn't do it for basic arithmetic when doing calculus of course, OTOH in algebra commutativity is not to be assumed...) Of course teachers/researchers didn't always follow these best practices themselves...