I'm not sure I understand. There is not a proof needed. Is that not almost the very definition of two?
I guess 1+1=2 is a convention.
if a single entity is called 1 (conventionally) then its double will be called 2(conventionally). since two quantities are individually single therfor 1+1=2 must hold. [for this operation of addition is also defined conventionally.]
this question is similar to the question why B comes after A.(even it is a convention)