Verb tenses in hypothetical situations

Question

I'm wondering how Japanese tenses work for hypothetical situations that may happen or could have happened.

More specifically, are the verb tenses in the below sentences correct?

We probably would not have come this far without his support.

彼の支援がなかったら、ここまで進んでなかったでしょう。

If you don't hurry, you will be late for school.

急がないと遅刻するよ

I have seen this post as well, but I'm wondering about present and future situations as well.

Answer 1

Yes, you are very correct. ~ないと is a very common usage for hypothetical future tense.

I would like to just point out that in your first past tense that the "if" is actually implied by なかったら in the prior phrase, not なかった in the second, like so:

彼の支援がなかったら、ここまで進んでなかったでしょう。

and my translation

If it were not for his support, we probably would not have come this far.