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# C++ concepts: LessThanComparable

From cppreference.com
< cpp‎ | concept

The type must work with < operator and the result should have standard semantics.

### [edit] Requirements

The type `T` satisfies `LessThanComparable` if

Given

- `a`, `b`, and `c`, expressions of type `T` or `const T`

The following expressions must be valid and have their specified effects

Expression | Return type | Requirements
--- | --- | ---
a < b | implicitly convertible to bool | Establishes strict weak ordering relation with the following properties For all `a`, !(a < a) If a < b then !(b < a) if a < b and b < c then a < c

### [edit] Notes

To satisfy this requirement, types that do not have built-in comparison operators have to provide a user-defined operator<

For the types that are both `EqualityComparable` and `LessThanComparable`, the C++ standard library makes a distinction between equality, which is the value of the expression a == b and equivalence, which is the value of the expression !(a < b) && !(b < a).

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