From CLRS (third edition, page 19), there is a footnote:
When the loop is a for loop, the moment at which we check the loop invariant just prior to the first iteration is immediately after the initial assignment to the loop-counter variable and just before the first test in the loop header.
Why is the checking moment specifically chosen to be after the initial assignment but before the first test? Note the excerpt is talking about proving correctness of algorithms using loop invariants.