Inversion of Order

http://www.englishgrammar.org/inversion-conditional-clauses/

Inversion in conditional clauses

Had it not rained

Contracted negative forms are not possible when we use an inverted word order to talk about an unreal or impossible situation in the past.

Had she not helped me I would have been in bad trouble. (NOT Hadn’t she helped me I would have been in bad trouble.)

This is actually the inverted form of the sentence ‘If she had not helped me I would have been in bad trouble’.

Had it not rained yesterday, we would have finished painting the walls.

Of course, contracted negative forms are possible when we use normal word order.

If it had not rained yesterday, we would have finished painting the walls. OR If it hadn’t rained yesterday, we would have finished painting the walls.

If you hadn’t been so stupid as to reject that job offer, youcould have attained financial independence now.

The third conditional sentences are used to talk about things that might have happened, but didn’t. Note that here we use a past perfect tense in the if-clause and would/could have + past participle in the main clause.

If it hadn’t rained yesterday, we would have hosted the party in the garden.

Should you not wish to

The inversion structure is also possible with should.

The structure with should is used to talk about present and future conditions. Here again negative forms are not contracted.

Should you not wish to join them, you must let them know before 4 o’clock. (NOT Shouldn’t you…)

Should you decide the sell the house, I will be happy to buy it from you.

Note that here should does not show obligation. It is merely used as an alternative to the present simple tense.

If you decide to sell the house, I will be happy to buy it from you.

Were we to have

Inversion is also possible with were. This structure is used to talk about the imaginary or improbable future situations.

Were we to have kids, we would need a bigger house. (= If we were to have kids, we would need a bigger house.)