Well, if we want to give an unclunky, simplified version of the above rule, then it would be something like,

"Gluing on the common elements \\(b\\) with the feasibility relations \\(\phi(a,b)\\) and \\(\psi(b,c)\\), and then gluing on the common elements \\(c\\) with \\(\nu(c,d)\\), is logically the same as gluing on the common elements \\(c\\) with the feasibility relations \\(\psi(b,c)\\) and \\(\nu(c,d)\\), and then gluing on the common elements \\(b\\), with the feasiblity relation \\(\phi(a,b)\\)."

"Gluing on the common elements \\(b\\) with the feasibility relations \\(\phi(a,b)\\) and \\(\psi(b,c)\\), and then gluing on the common elements \\(c\\) with \\(\nu(c,d)\\), is logically the same as gluing on the common elements \\(c\\) with the feasibility relations \\(\psi(b,c)\\) and \\(\nu(c,d)\\), and then gluing on the common elements \\(b\\), with the feasiblity relation \\(\phi(a,b)\\)."