Conditionals and inversion

In formal English, the subject and the auxiliary can be inverted in the if-clause with if omitted:

Should you see Kate, say hi from me. (if you should see Kate)
Were he to propose to you now, what would you say? (if he were to propose to you)
Were I you, I would stop smoking. (if I were you)
Were it not for Miguel, we wouldn't know what to do now. (if it weren't for Miguel)
Had we booked our flight earlier, it would have been cheaper. (if we had booked our flight earlier)
Had it not been for your foolishness, we wouldn't have got lost. (if it hadn't been for your foolishness)