I do not think there is any right or wrong in this discussion,
so I would not make any more comment on this topic for now.
Your interpretation that "(a cmp-op b) is an assertion on a" is
one valid interpretation of a boolean expression. I would
understand it if you say you are used to think of it as an
assertion about the left hand side. I just do not think of it
that way. Rather, to me, "(a cmp-op b)" (or an boolean
expression in any shape for that matter) as a whole is an
assertion, and it is simply easier for me if a and b are ordered
from left to right, to visually match ascending order.
But that is only because I am used to read programs written that
way. Just like you are used to think of these expressions about
assertions of the left hand side.