L is monotone.
Let L , M , N be non empty relational structures, f be a map from L into M , and g be a map from M into N . If f is monotone and g is monotone, then g f is monotone. Let L , M be non empty relational structures, f be a map from L into M , X be a subset of L , and x be an element of L . Let L , M be non empty relational structures, f be a map from L into M , X be a subset of L , and x be an element of L . Let S , T be non empty relational structures, f be a map from S into T , and X be a directed subset of S .