"It is straightforward to show that..." means that you could probably do it with your current knowledge, but it will take 6 dense pages, four false starts and about a week of focused work.
I used to joke that when a solution was known to exist the problem was "trivial"; when a solution was not known to exist it was "nontrivial". A problem that's bloody well impossible is "decidedly nontrivial".
'You' being personified here, rather than the general you.
Straightforward tends to suggest we don't have to have a bunch of meetings about it, because the right person either has the knowledge or we know precisely where to get it.