You can also think of A5 in terms of its contrapositive: For all A,B∈L, if A≻B, then for all 0<p≤1A≻pA+(1−p)B
This is basically just the strict version of A4. I probably should have written it that way instead. I wanted to use ⪰ instead of ≻, because it is closer to the base definition, but that is not how I was natively thinking about it, and I probably should have written it the way I think about it.
You can also think of A5 in terms of its contrapositive: For all A,B∈L, if A≻B, then for all 0<p≤1A≻pA+(1−p)B
This is basically just the strict version of A4. I probably should have written it that way instead. I wanted to use ⪰ instead of ≻, because it is closer to the base definition, but that is not how I was natively thinking about it, and I probably should have written it the way I think about it.