I was picking where to eat dinner, and this logic question arose. Because I didn't want to dine at the same place twice in a single day.
Let me call the restaurant "Kim's". The following statement is obviously true:
Since I dined at Kim's once, I'd be able to dine at Kim's twice.
The following statement is also true, which seems to be some sort of "dual" to the statement above:
Since I dined at Kim's twice, I must've dined at Kim's once.
At my first glance, some sort of modality seems to be in action. I'd like to formally prove the equivalence between these statements. However, because of the presence of complex auxiliary verbs, it's hard to identify what kind of modal logic is this. As such, I can't even formally formulate these statements.
Note that this problem can be demonstrated in another language. Here's one instance in Korean, my native language:
내가 김가네에서 한 번 식사했으니, 김가네에서 두 번 식사할 수도 있겠다.
내가 김가네에서 두 번 식사했으니, 김가네에서 한 번 식사했었겠다.