They are necessarily non-constructive existence proofs, for sure. You're not alone in some potential unease with that: https://en.wikipedia.org/wiki/Constructiv

They are necessarily non-constructive existence proofs, for sure. You're not alone in some potential unease with that: https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics) https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...