Distribution of multiplied variable into min() function Is distributing a variable over a $min$ call ($i \times min({1  \over i}, {1 \over j}) = min({i \over i}, {i \over j})$ correct? Intuitively it is, but I can find no difinitive answer.
PS - if anyone is curious/kind enough to read the context, I include it as a comment.

Yes, it is correct.
This is due to $i$ is non-negative.
If $b \le c$ and $a \ge 0$, then we have $ab \le ac$.
