@@ -89,8 +89,8 @@ lemma emultiplicity_eq_of_valuation_eq_ofAdd {a : A} {k : ℕ}
8989 have hnz : a ≠ 0 := ne_zero_of_some_le_intValuation _ (le_of_eq hv.symm)
9090 have hnb : Ideal.span {a} ≠ ⊥ := by
9191 rwa [ne_eq, Ideal.span_singleton_eq_bot]
92- simp only [intValuation_if_neg _ hnz, ofAdd_neg, WithZero.coe_inv, inv_inj, WithZero.coe_inj ,
93- EmbeddingLike.apply_eq_iff_eq, Nat.cast_inj] at hv
92+ simp only [intValuation_if_neg _ hnz, WithZero.exp, ofAdd_neg, WithZero.coe_inv, inv_inj,
93+ WithZero.coe_inj, EmbeddingLike.apply_eq_iff_eq, Nat.cast_inj] at hv
9494 rw [← hv, UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors v.irreducible hnb,
9595 count_associates_factors_eq hnb v.isPrime v.ne_bot, normalize_eq]
9696
@@ -117,7 +117,7 @@ lemma exists_adicValued_mul_sub_le {a b : A} {γ : WithZero (Multiplicative ℤ)
117117 (emultiplicity_eq_of_valuation_eq_ofAdd v <| intValuation_eq_coe_neg_multiplicity v hnz)
118118 (ENat.coe_le_coe.mpr hle)
119119 have hb : b ∈ v.asIdeal ^ multiplicity v.asIdeal (Ideal.span {a}) := by
120- rwa [← intValuation_le_pow_iff_mem, ← intValuation_eq_coe_neg_multiplicity _ hnz]
120+ rwa [← intValuation_le_pow_iff_mem, WithZero.exp, ← intValuation_eq_coe_neg_multiplicity _ hnz]
121121 -- Now make use of
122122 -- `v.asIdeal ^ multiplicity v.asIdeal (Ideal.span {a}) = v.asIdeal ^ n ⊔ Ideal.span {a}`
123123 -- (this is where we need `IsDedekindDomain A`)
@@ -127,7 +127,7 @@ lemma exists_adicValued_mul_sub_le {a b : A} {γ : WithZero (Multiplicative ℤ)
127127 obtain ⟨y, hy⟩ := Ideal.mem_span_singleton'.mp hz
128128 use y
129129 -- And again prove the result about valuations by turning into one about ideals.
130- rwa [hy, ← hxz, sub_add_cancel_right, intValuation_le_pow_iff_mem, neg_mem_iff]
130+ rwa [hy, ← hxz, sub_add_cancel_right, ← WithZero.exp, intValuation_le_pow_iff_mem, neg_mem_iff]
131131
132132lemma exists_adicValued_sub_lt_of_adicValued_le_one {x : (WithVal (v.valuation K))}
133133 (γ : (WithZero (Multiplicative ℤ))ˣ) (hx : Valued.v x ≤ 1 ) :
@@ -432,7 +432,7 @@ theorem exists_uniformizer (v : HeightOneSpectrum A) :
432432 ∃ π : v.adicCompletionIntegers K, Valued.v π.1 = Multiplicative.ofAdd (- 1 : ℤ) := by
433433 obtain ⟨π, hπ⟩ := v.intValuation_exists_uniformizer
434434 use π
435- rw [← hπ, ← ValuationSubring.algebraMap_apply, ← IsScalarTower.algebraMap_apply,
435+ rw [← WithZero.exp, ← hπ, ← ValuationSubring.algebraMap_apply, ← IsScalarTower.algebraMap_apply,
436436 v.valuedAdicCompletion_eq_valuation, v.valuation_of_algebraMap]
437437
438438variable {K} in
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