Set comparisons

bool contains(const T& v) const; 
bool contains(const interval<T>& o) const; 
bool overlaps(const interval<T>& o) const;

These functions make set assertions by comparison to an other $KR$ or $R$ value.

contains(const T&): Determines whether the given $R$ value is contained in the current interval.
contains(const kaucher_interval<T>&): Determines whether the given interval is fully inside and contained in the current interval.
overlaps(const kaucher_interval<T>&): Determines whether the given interval overlaps with the current interval but is not fully contained in the latter.