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Showing content from https://en.cppreference.com/w/cpp/language/../named_req/ForwardIterator.html below:

C++ named requirements: LegacyForwardIterator - cppreference.com

A LegacyForwardIterator is a LegacyIterator that can read data from the pointed-to element.

Unlike LegacyInputIterator and LegacyOutputIterator, it can be used in multipass algorithms.

If a LegacyForwardIterator it originates from a Container, then it's value type is the same as the container's, so dereferencing (*it) obtains the container's value type.

X satisfies LegacyForwardIterator if all following conditions are satisfied:

• X satisfies LegacyInputIterator.
• X satisfies DefaultConstructible.
• If X is a mutable iterator, Ref is a reference to T.
• If X is a constant iterator, Ref is a reference to const T.
• Objects of the type X provide multi-pass guarantee.
• If i and j are equal, then either i and j are both dereferenceable or else neither is dereferenceable.
• If i and j are both dereferenceable, then i == j if and only if *i and *j are bound to the same object.
• The following expressions must be valid and have their specified effects:

The domain of == for forward iterators is that of iterators over the same underlying sequence.

However, value-initialized forward iterators can be compared, and must compare equal to other value-initialized iterators of the same type.

In other words, value-initialized forward iterators behave as if they refer past the end of the same empty sequence.

Two dereferenceable iterators a and b of type X offer the multi-pass guarantee if all following conditions are satisfied:

• a == b implies ++a == ++b.
• Any of the following conditions is satisfied:

• X is a pointer type.
• The expression (void)++X(a), *a is equivalent to the expression *a.

For the definition of std::iterator_traits, the following exposition-only concept is defined.

where the exposition-only concept __LegacyInputIterator<T> is described in LegacyInputIterator.

Unlike the std::forward_iterator concept, the LegacyForwardIterator requirements requires dereference to return a reference.

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

1. ↑ In the scenario where a and b use the same underlying iterator, evaluating the expression ++a == ++b actually increments the underlying container twice, but the result is still true.
2. ↑ Formally also requires implying ++b != a.

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