Each element of a monoid has exactly one inverse element.

A lattice has one top at most.

A lattice has one bottom at most.

The identity of a group is unique.

A non-empty subset of an ordered set has one supremum at most.

A non-empty subset of an ordered set has one infimum at most.

An ordered set has one greatest element at most.

An ordered set has one smallest element at most.

The empty set is unique.

An algebraic structure has one zero element at most.

An algebraic structure has one identity element at most.