x_{1} is a binary relation which is right-Euclidean on space/set/under conditions x_{2}.

Definitionally, x_{1} is an ordered binary relation given by set R such that for all a, b, c in x_{2} (if such makes sense; else: the universe of discourse restricted by x_{2}), if (a, b) in R and (a, c) in R, then (b, c) in R and (c, b) in R. See also: "takni", ".efklizu".