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[Merged by Bors] - perf(RingTheory/Artinian): reorder arguments in IsArtinianRing.isMaximal_of_isPrime #21449

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[Merged by Bors] - perf(RingTheory/Artinian): reorder arguments in IsArtinianRing.isMaximal_of_isPrime #21449

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5 changes: 4 additions & 1 deletion Mathlib/RingTheory/Artinian/Module.lean
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Expand Up @@ -485,7 +485,10 @@ lemma isField_of_isDomain [IsDomain R] : IsField R := by

/- Does not hold in a commutative semiring:
consider {0, 0.5, 1} with ⊔ as + and ⊓ as *, then both {0} and {0, 0.5} are prime ideals. -/
instance isMaximal_of_isPrime (p : Ideal R) [p.IsPrime] : p.IsMaximal :=
-- Note: type class synthesis should try to synthesize `p.IsPrime` before `IsArtinianRing R`,
-- hence the argument order.
instance isMaximal_of_isPrime {R : Type*} [CommRing R] (p : Ideal R) [p.IsPrime]
[IsArtinianRing R] : p.IsMaximal :=
Ideal.Quotient.maximal_of_isField _ (isField_of_isDomain _)

lemma isPrime_iff_isMaximal (p : Ideal R) : p.IsPrime ↔ p.IsMaximal :=
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