For a finite free extension of DVRs `O → Oδ` of rank `δ` in which a uniformizer stays irreducible, `K ⊗_O Oδ` is a field of degree `δ` over `K` and a fraction field of `Oδ`.

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For a finite free extension of DVRs `O → Oδ` of rank `δ` in which a uniformizer stays irreducible, `K ⊗_O Oδ` is a field of degree `δ` over `K` and a fraction field of `Oδ`. · Prove2Me