I did so vs So did I

[Sup3rm4n]

Hi there Grammarians !!

I'm working on this paradigme, the function and use of the verb do in these two sentences.

[1] I did so
[2] So did I

I came out to the conclusion that in I did so, do is a full verb, pro-verb, whereas in So did I, it is an auxiliary.

Can somebody back this up, or am I off the track??

Thank you

SUp3rm4n

[Alan]

Hi,

I agree.

Alan
_________________
English as a Second Language
You can read my ESL story Present Simple

[Jeongsil Song]

Your conclusion is correct.
Do in I did so is a full verb, as evidenced by "I'm doing so," "I have done so," "I'd like to do so," etc. in which do is oviously used as a full verb.
Do in So did I is an auxiliary, just as in the same other structural patterns like "So can I," "So must I," etc. can and must are auxiliaries.