Using std::is_convertible with std::type_index

I have an vector of std::type_index, which indicate the trait types that a particular node has. I'm implementing a function which checks whether the node supports a particular type. It looks like this:

std::vector<std::type_index> traits;

...

template <typename T>
bool hasTrait() {
    return std::find(traits.begin(), traits.end(), typeid(T)) != traits.end();
}

However, this won't work if type T is a derived type of some base type in traits. In order to fix this problem, I wanted to use std::is_convertible.

However, I only have access to the std::type_index of the type, so I can't do that. Something like this would be required: std::is_convertible<traitTypeIndex::type, T>