Domains and inequality consistency

[matbesancon]

Suppose that you have a set defined as:
x | x >= 0 & f(x) <= 0

with dom(f) = {x | x >= 0}, this implies f(x) cannot be computed if x >= 0.
A first idea was to compute a distance as

if x < 0
    abs(x)
else
    max(f(x), 0)
end

This can result in consistency issues (still haven't formally written down how it appears)