Over a discrete valuation ring `R` with fraction field `K`, a monic polynomial `A` and a polynomial `B` reducing to `1` modulo the maximal ideal are coprime over `K`.

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Over a discrete valuation ring `R` with fraction field `K`, a monic polynomial `A` and a polynomial `B` reducing to `1` modulo the maximal ideal are coprime over `K`. · Prove2Me