Improved Lower Bound for Frankl’s Union-Closed Sets Conjecture

We verify an explicit inequality conjectured in Gilmer, 2022, arXiv: 2211. 09055, thus proving that for any nonempty union-closed family F 2^n, some i n is contained in at least a 3-52 0. 38 fraction of the sets in F \. One case, an explicit one-variable inequality, is checked by computer calculation.