"do" and "have"

[twinkle]

Hello,

I'm somewhat confused with the usage of "do" and "have" in certain cases; Please give advise.

Even if it did work... ( is did in this case subjunctive mood?)



1.
My neighbour has had more tomatoes than I have (had).

2.
My neighbour had more tomatoes than I did.

Why do we use "have" in the first sentence and "do" in the second?

Thank you very much

Maybe my question was too unprecise.

In the first and second sentence the "I have" and "I did" respectively are short forms, we can use them instead of "My neighbour has had more tomatoes than I have had tomatoes" or "My neighbour had more tomatoes than I had tomatoes". Am I wrong? But why must we use "do" for the second and "have" for the first abbreviation?

Is it because "has" in "has had" is an auxiliary verb, while "had" in "neighbour had" isn't?