My new result, proved with advanced funcoids theory (and never tried to prove it with basic general topology): Whether a uniformity on a topology is normal is determined by the proximity induced by the uniformity. (Moreover I expressed it as an explicit algebraic formula in terms of funcoids: $\nu\circ\nu^{-1}\sqsubseteq\nu^{-1}\circ\mu$, where $\mu$ is the proximity induced by the quasi-uniformity and $\nu$ is the topological space).