Estonia (which has internet based voting) solves this by letting you check your vote on a different device but for only a short time period.
The thinking is that even if someone has managed to compromise, say, your laptop (e.g. through a specially constructed virus) to secretly switch your vote to a different party, then they'd also need to be able to compromise your phone too to persuade an entirely different piece of software to also report your vote back to you wrongly. Not impossible, but a much harder task (especially as you'd need to manage to do it for everyone, or else there'll be a big outcry from the large number of people who notice a discrepancy).
Being able to prove you voted that way during that time period doesn't really matter, as the system already allows you vote as many times as you like, with only the last one being counted. (i.e. if someone tries to coerce you, or buy your vote, you simply vote their way, and then, when they head off to the next person, log back in again and vote the way you originally wanted.)
The thinking is that even if someone has managed to compromise, say, your laptop (e.g. through a specially constructed virus) to secretly switch your vote to a different party, then they'd also need to be able to compromise your phone too to persuade an entirely different piece of software to also report your vote back to you wrongly. Not impossible, but a much harder task (especially as you'd need to manage to do it for everyone, or else there'll be a big outcry from the large number of people who notice a discrepancy).
Being able to prove you voted that way during that time period doesn't really matter, as the system already allows you vote as many times as you like, with only the last one being counted. (i.e. if someone tries to coerce you, or buy your vote, you simply vote their way, and then, when they head off to the next person, log back in again and vote the way you originally wanted.)