Composition of binary relations can be decomposed into two operations: and :
Composition of binary relations is decomposed as: .
I introduce similar decomposition of reloids, and using this try to prove that composition with a principal reloid is distributive over join of reloids.
The proof is partial, there are some white spots in it. The idea is very elegant, but I have failed to make a complete proof. Please email me or comment on this blog if you find a complete proof.
See this note about the proof (PDF).