Set assertions

7.4.1 Set assertions

bool disjoint(const kaucher_interval<T>& a, const kaucher_interval<T>& b); 
bool proper_subset(const kaucher_interval<T>& a, const kaucher_interval<T>& b); 
bool subset(const kaucher_interval<T>& a, const kaucher_interval<T>& b); 
bool proper_superset(const kaucher_interval<T>& a, const kaucher_interval<T>& b); 
bool superset(const kaucher_interval<T>& a, const kaucher_interval<T>& b); 
bool overlap(const kaucher_interval<T>& a, const kaucher_interval<T>& b);

disjoint(const kaucher_interval<T>& a, const kaucher_interval<T>& b): Determines whether the two given intervals are disjoint to each other, that is whether they do not have any common set.
proper_subset(const kaucher_interval<T>& a, const kaucher_interval<T>& b): Determines whether $A$ is a proper subset of $B$ , that is $A ⊂ B$ .
subset(const kaucher_interval<T>& a, const kaucher_interval<T>& b): Determines whether $A$ is a subset of $B$ , that is $A ⊆ B$ .
proper_superset(const kaucher_interval<T>& a, const kaucher_interval<T>& b): Determines whether $A$ is a proper superset of $B$ , that is $A ⊃B$ .
superset(const kaucher_interval<T>& a, const kaucher_interval<T>& b): Determines whether $A$ is a superset of $B$ , that is $A ⊇ B$ .
overlap(const kaucher_interval<T>& a, const kaucher_interval<T>& b): Determines whether the ranges of $A$ and $B$ overlap to any degree.

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