This question already has an answer here:
I did use to live in London.
I did used to live in London.
Which one is correct?
According to the usage of emphatic do with past tense (eg "I lived in London/I did live in London"), did should change ‘used to’ to ‘use to,’ but I didn't find anything about it except in English Grammar Today by Cambridge. However, Cambridge used did with ‘used to.’ Shouldn't emphatic did change ‘used to’ to ‘use to’?
From English Grammar Today
We can use the emphatic auxiliary did with used to:
We never used to mix very much with the neighbours, but we did used to say hello to them in the street. (Don't use this form in written exams.)