The following comes from Definition 2 in Pavel Pudlak, "A new proof of the congruence lattice representation theorem," *Algebra Universalis* **6** (1976), 269-275.

Let $X$ be a set.  Let $F$ be a family of functions from $X$ to itself containing the identity map and closed under composition.

Define a binary relation on the family of one- or two-element subsets of $X$ as follows.  Let $a,b,c,d\in X$.  We will say that $\{a,b\}$ *dominates* $\{c,d\}$ if there are $n\in\mathbb N_0$, $u_0,\dots,u_n\in X$, and $f_1,\dots,f_n\in F$ such that $u_0=c$, $u_n=d$, and $\{f_i(a),f_i(b)\}=\{u_{i-1},u_i\}$ for $i=1,\dots,n$.

Why is domination transitive?