Alternatives for "For the sake of completeness"?

I'd like to include in a paper on mathematics the phrase:

"for the sake of completeness, we first show..."

or words to that effect. However, the word "completeness" has a precise technical interpretation in mathematics and so I'd prefer not to use it. Any suggestions for alternatives?

Solution 1:

Something along the line "To cover every aspect, we show..." would help you out. If you want to avoid the word "cover", as it has a mathematical meaning, use "To deal with every aspect, we show..." instead which is less elegant, but causes no complications with mathematical terms.

Solution 2:

In a paper on mathematics, you might say

"For the sake of rigor, we first show..."

The concept of mathematical rigor is discussed here.