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chore(NumberTheory): golf inftyValuation.polynomial (#30979)
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Mathlib/NumberTheory/FunctionField.lean

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@@ -216,8 +216,7 @@ theorem inftyValuation.X_inv : inftyValuation Fq (1 / RatFunc.X) = exp (-1) := b
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-- https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/.60synthInstance.2EmaxHeartbeats.60.20error.20but.20only.20in.20.60simpNF.60
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theorem inftyValuation.polynomial {p : Fq[X]} (hp : p ≠ 0) :
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inftyValuationDef Fq (algebraMap Fq[X] (RatFunc Fq) p) = exp (p.natDegree : ℤ) := by
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have hp' : algebraMap Fq[X] (RatFunc Fq) p ≠ 0 := by simpa
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rw [inftyValuationDef, if_neg hp', RatFunc.intDegree_polynomial]
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rw [inftyValuationDef, if_neg (by simpa), RatFunc.intDegree_polynomial]
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/-- The valued field `Fq(t)` with the valuation at infinity. -/
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def inftyValuedFqt : Valued (RatFunc Fq) ℤᵐ⁰ :=

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