Euclidean relation
= Euclidean relation
{c}
{title2=$xRy\land xRz\implies yRz$}
{wiki}
A <binary relation> is right Euclidean when any two successors of the same element are related in the indicated order. A <reflexive relation> with this property is an <equivalence relation>: reflexivity gives symmetry, and symmetry followed by the Euclidean property gives transitivity. Without reflexivity, even the empty <binary relation> is Euclidean.