Erdős Problem 869

### What is the conjecture

https://www.erdosproblems.com/869

If $A_1,A_2$ are disjoint additive bases of order $2$ (i.e. $A_i+A_i$ contains all large integers) then must $A=A_1\cup A_2$ contain a minimal additive basis of order $2$ (one such that deleting any element creates infinitely many $n\not\in A+A$)?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading the linked Erdős Problem 869 statement and surveying existing formalized conjectures in the formal-conjectures repository. Determine the appropriate place and conventions for this conjecture; done means its statement is added in Lean with the repository's expected validation passing.

Written by the indexing model from the issue text.