On the task formulated in this blog post:

An attempt to prove that $\mathrm{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ is closed under finite intersections (see http://portonmath.tiddlyspace.com/#%5B%5BSingularities%20funcoids%3A%20some%20special%20cases%5D%5D)

http://portonmath.tiddlyspace.com/#%5B%5BSingularities%20funcoids%3A%20special%20cases%20proof%20attempts%5D%5D