# C++ concepts: LessThanComparable

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< cpp‎ | concept

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

### 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
- Defining equiv(a, b) as !(a < b) && !(b < a), if equiv(a, b) and equiv(b, c), then equiv(a, c)

### 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).

### See also

Compare | a `BinaryPredicate` that establishes an ordering relation (concept)

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