Proof equality in some dependent type theories such as CoC do not care about the internals. All proofs of a certain proposition are equal, same for different proofs between equal propositions. This clearly shows that internals do not actually matter in such dependent type theories. Heck, internals do not even matter in type theories with universes (where different proofs of the same proposition are not necessarily equal) - if you do not have typecase all proofs of the proposition (t : *) -> t -> t are equal for example.
Dependent types are what we need in order to ignore the internals and focus on what matters.