Original sentence: For example, it is equivalent to the condition that for every x in S there exists an  element x’ such that x’xx’ = x’,  xx’x = x, ( xx’ )* = xx’, ( x’x )* = x’x
Edited sentence: An axiomatic definition is the condition that for every x in S there exists an  element x’ such that x’xx’ = x’,  xx’x = x, ( xx’ )* = xx’, ( x’x )* = x’x.Another is to say that every L-class contains a projection