Set assertions

5.4.1 Set assertions

bool disjoint(const interval<T>& a, const interval<T>& b); 
bool proper_subset(const interval<T>& a, const interval<T>& b); 
bool subset(const interval<T>& a, const interval<T>& b); 
bool proper_superset(const interval<T>& a, const interval<T>& b); 
bool superset(const interval<T>& a, const interval<T>& b); 
bool interior(const interval<T>& a, const interval<T>& b); 
bool overlap(const interval<T>& a, const interval<T>& b); 
 
bool inside(const interval<T>& a, const T& v);

disjoint(const interval<T>& a, const 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 interval<T>& a, const interval<T>& b): Determines whether $A$ is a proper subset of $B$ , that is $A ⊂ B$ .
subset(const interval<T>& a, const interval<T>& b): Determines whether $A$ is a subset of $B$ , that is $A ⊆ B$ .
proper_superset(const interval<T>& a, const interval<T>& b): Determines whether $A$ is a proper superset of $B$ , that is $A ⊃B$ .
superset(const interval<T>& a, const interval<T>& b): Determines whether $A$ is a superset of $B$ , that is $A ⊇ B$ .
interior(const interval<T>& a, const interval<T>& b): Determines whether $A$ is in inside of the convex hull of $B$ , that is $◦ A∈ B$
overlap(const interval<T>& a, const interval<T>& b): Determines whether the ranges of $A$ and $B$ overlap to any degree.
inside(const interval<T>& a, const T& v): Determines whether the given value $v$ is contained inside $A$ , that is whether $v∈ A$ .

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