Auxiliary verbs - ellipsis

I don't like action movies but Andy does.
I 'm not going to the party but Mandy is.
She thought she 'd locked the door but she hadn't.
In the examples above, the auxiliaries are used to make the sentences shorter. If we didn't use auxiliaries in this way we would have to repeat some words. I don't like action movies but Andy likes action movies.
I'm not going to the party but Mandy is going to the party.
She thought she 'd locked the door but she hadn't locked the door. We could shorten the second part by using pronouns, but the sentences would still contain a repeated verb and this can sound clumsy in English. I don't like action movies but Andy likes them.
I'm not going to the party but Mandy is going there.
She thought she 'd locked the door but she hadn't locked it.

When the first part of the sentence - the part we don't want to repeat - contains an auxiliary, we use that auxiliary in the second part. Auxiliary verb have
I have never been to Australia but Donna has. Auxiliary verb did
I didn't see the film but the others did.

When the first part of the sentence - the part we don't want to repeat - does not contain an auxiliary (e.g. when we use present simple or past simple), we use do / does (present simple) and did (past simple) in the second part. Present simple
I like action movies but my brother doesn't. Past simple
I went to the party but Sarah didn't.

When the main verb is be, we can also avoid repetition in this way.
'Were you at the meeting yesterday?'
'I wasn't but Sandy was.'