Context { valid_exp : Valid_exp fexp }.

Lemma fexp_negligible_exp_eq: forall n m, (n <= fexp n)%Z -> (m <= fexp m)%Z -> fexp n = fexp m.
Definition ulp x := match Req_bool x 0 with
| true   => match negligible_exp with
| Some n => bpow (fexp n)
| None => 0%R
end
| false  => bpow (canonic_exp beta fexp x)
end.