LW · GW
The use of Chu spaces is very interesting. This is also a great introduction to Chu spaces.
I was able to formalize the example in the research automated theorem prover Avalog: https://github.com/advancedresearch/avalog/blob/master/source/chu_space.txt
It is still very basic, but shows potential. Perhaps Avalog might be used to check some proofs about Cartesian frames.