Value comparison

5.5.2 Value comparison

bool veq(const interval<T>&, const interval<T>&); 
bool vne(const interval<T>&, const interval<T>&); 
bool vle(const interval<T>&, const interval<T>&); 
bool vge(const interval<T>&, const interval<T>&); 
bool vlt(const interval<T>&, const interval<T>&); 
bool vgt(const interval<T>&, const interval<T>&);

Value comparison operators treat the given intervals as if they were a single number. Empty intervals of $∅$ are explicitly considered valid. That is for $X,Y ∈ IR$ and $□∈ {=,<,≤,>,≥}$ :

X□Y ≡ (∀a∈ X,∃b∈ Y :a□b)

A special case is for inequality $̸=$ which is the same as above but using a disjunction instead of a conjunction, that is:

X ̸= Y ≡ (∀a∈ X,∃b∈ Y :a ̸=b)

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