  Gunby-He-Narayanan showed that the logarithmic gap predictions of Kahn-Kalai
and Talagrand (proved by Park-Pham and Frankston-Kahn-Narayanan-Park) about
thresholds of up-sets do not apply to down-sets. In particular, for the
down-set of triangle-free graphs, they showed that there is a polynomial gap
between the threshold and the factional expectation threshold. In this short
note we give a simpler proof of this result, and extend the polynomial
threshold gap to down-sets of F-free graphs.
